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NONLINEAR RIEMANN AND HILBERT BOUNDARY VALUE PROBLEMS WITH SQUARE ROOTS IN VARIABLE EXPONENT SPACES 认领 引用
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作者 Yajun Hu Fuli He 《Acta Mathematica Scientia》 SCIE CSCD 2026年第1期1-18,共18页
In this paper,we study the nonlinear Riemann boundary value problem with square roots that is represented by a Cauchy-type integral with kernel density in variable exponent Lebesgue spaces.We discuss the odd-order zer... In this paper,we study the nonlinear Riemann boundary value problem with square roots that is represented by a Cauchy-type integral with kernel density in variable exponent Lebesgue spaces.We discuss the odd-order zero-points distribution of the solutions and separate the single valued analytic branch of the solutions with square roots,then convert the problem to a Riemann boundary value problem in variable exponent Lebesgue spaces and discuss the singularity of solutions at individual zeros belonging to curve.We consider two types of cases those where the coefficient is Hölder and those where it is piecewise Hölder.Then we solve the Hilbert boundary value problem with square roots in variable exponent Lebesgue spaces.By discussing the distribution of the odd-order zero-points for solutions and the method of symmetric extension,we convert the Hilbert problem to a Riemann boundary value problem.The equivalence of the transformation is discussed.Finally,we get the solvable conditions and the direct expressions of the solutions in variable exponent Lebesgue spaces. 展开更多
关键词 boundary value problem Cauchy-type integral variable exponent spaces non-linearity piecewise Lyapunov curve
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Nonlocal Boundary Value Problems for Nonlinear Fractional Differential Equations with a Disturbance Parameter on the Infinite Interval 认领 引用
2
作者 ZHENG Yanping YANG Hui WANG Wenxia 《应用数学》 北大核心 2026年第2期360-372,共13页
This paper is concerned with a class of nonlinear fractional differential equations with a disturbance parameter in the integral boundary conditions on the infinite interval.By using Guo-Krasnoselskii fixed point theo... This paper is concerned with a class of nonlinear fractional differential equations with a disturbance parameter in the integral boundary conditions on the infinite interval.By using Guo-Krasnoselskii fixed point theorem,fixed point index theory and the analytic technique,we give the bifurcation point of the parameter which divides the range of parameter for the existence of at least two,one and no positive solutions for the problem.And,by using a fixed point theorem of generalized concave operator and cone theory,we establish the maximum parameter interval for the existence of the unique positive solution for the problem and show that such a positive solution continuously depends on the parameter.In the end,some examples are given to illustrate our main results. 展开更多
关键词 Boundary value problem Disturbance parameter Infinite interval Bifurcation point Cone
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Ambrosetti-Prodi Type Results for the Discrete Boundary Value Problems Involving the Singularφ-Laplacian 认领 引用
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作者 Yanyun LI Man XU 《Journal of Mathematical Research with Applications》 CSCD 2025年第6期773-788,共16页
In this paper,we consider the discrete boundary value problem of the type{∆u1=0=∆un-1,∇(tkN-1)φ(∆uk))+tkN-1fk(tk,uk,∆uk)=0,2≤k≤n-1,whereφ:(-a,a)→R,0<a<∞,is an increasing homeomorphism ... In this paper,we consider the discrete boundary value problem of the type{∆u1=0=∆un-1,∇(tkN-1)φ(∆uk))+tkN-1fk(tk,uk,∆uk)=0,2≤k≤n-1,whereφ:(-a,a)→R,0<a<∞,is an increasing homeomorphism withφ(0)=0,such aφis called singular,N≥1,n≥3 are integers,tk are the grid points,uk:=u(tk),k=1,2,...,n,∇is the backward difference operator defined by∆uk=uk-uk-1,△is the forward difference operator defined by△uk=uk+1-uk,fk(2≤k≤n-1)are continuous functions.We prove the existence of solutions to this problem by employing the sign condition,the continuation lemma and the upper and lower solutions,respectively.On this basis,we also establish the Ambrosetti-Prodi type results for it. 展开更多
关键词 singularφ-Laplacian discrete boundary value problem existence Ambrosetti-Prodi type results lower and upper solutions topological degree
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EXISTENCE RESULTS FOR SEMIPOSITONE BOUNDARY VALUE PROBLEMS 认领 引用 被引量：11
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作者 马如云 王汝发 任立顺 《Acta Mathematica Scientia》 SCIE 2001年第2期189-195,共7页
The authors study the existence of positive solutions to the boundary value problem where f and e: [r,R] x [0,∞) → R are two continuous functions satisfying f 0 and |e| M for some M > 0. The authors show that the... The authors study the existence of positive solutions to the boundary value problem where f and e: [r,R] x [0,∞) → R are two continuous functions satisfying f 0 and |e| M for some M > 0. The authors show that there exists at least one positive solution in the following two cases: (i) f is superlinear at infinity and λ > 0 is small enough; (ii) f is sublinear at infinity and λ > 0 is large enough. Their proofs are based on fixed point theorems in cones. 展开更多
关键词 Existence positive solution boundary value problem cone
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A CLASS OF NONLOCAL BOUNDARY VALUE PROBLEMS OF NONLINEAR ELLIPTIC SYSTEMS IN UNBOUNDED DOMAINS 认领 引用 被引量：65
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作者 莫嘉琪 欧阳成 《Acta Mathematica Scientia》 SCIE 2001年第1期93-97,共5页
The nonlocal boundary value problems for nonlinear elliptic systems in the unbounded domain are considered. Under suitable conditions the existence of solution and comparison theorem for the boundary value problems ar... The nonlocal boundary value problems for nonlinear elliptic systems in the unbounded domain are considered. Under suitable conditions the existence of solution and comparison theorem for the boundary value problems are studied. 展开更多
关键词 elliptic system boundary value problem comparison theorem
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Dirac method for nonlinear and non-homogenous boundary value problems of plates 认领 引用 被引量：3
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作者 Xiaoye MAO Jiabin WU +2 位作者 Junning ZHANG Hu DING Liqun CHEN 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI CSCD 2024年第1期15-38,共24页
The boundary value problem plays a crucial role in the analytical investigation of continuum dynamics. In this paper, an analytical method based on the Dirac operator to solve the nonlinear and non-homogeneous boundar... The boundary value problem plays a crucial role in the analytical investigation of continuum dynamics. In this paper, an analytical method based on the Dirac operator to solve the nonlinear and non-homogeneous boundary value problem of rectangular plates is proposed. The key concept behind this method is to transform the nonlinear or non-homogeneous part on the boundary into a lateral force within the governing function by the Dirac operator, which linearizes and homogenizes the original boundary, allowing one to employ the modal superposition method for obtaining solutions to reconstructive governing equations. Once projected into the modal space, the harmonic balance method(HBM) is utilized to solve coupled ordinary differential equations(ODEs)of truncated systems with nonlinearity. To validate the convergence and accuracy of the proposed Dirac method, the results of typical examples, involving nonlinearly restricted boundaries, moment excitation, and displacement excitation, are compared with those of the differential quadrature element method(DQEM). The results demonstrate that when dealing with nonlinear boundaries, the Dirac method exhibits more excellent accuracy and convergence compared with the DQEM. However, when facing displacement excitation, there exist some discrepancies between the proposed approach and simulations;nevertheless, the proposed method still accurately predicts resonant frequencies while being uniquely capable of handling nonuniform displacement excitations. Overall, this methodology offers a convenient way for addressing nonlinear and non-homogenous plate boundaries. 展开更多
关键词 rectangular plate Dirac operator nonlinear boundary time-dependent boundary boundary value problem
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MULTIPLE POSITIVE SOLUTIONS OF SINGULAR THIRD-ORDER PERIODIC BOUNDARY VALUE PROBLEM 认领 引用 被引量：22
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作者 孙经先 刘衍胜 《Acta Mathematica Scientia》 SCIE 2005年第1期81-88,共8页
This paper deals with the singular nonlinear third-order periodic boundary value problem u'' + p(3)u = f (t, u), 0 less than or equal to t less than or equal to 2pi, with u((i)) (0) = u((i)) (2pi), i = 0, 1, 2... This paper deals with the singular nonlinear third-order periodic boundary value problem u'' + p(3)u = f (t, u), 0 less than or equal to t less than or equal to 2pi, with u((i)) (0) = u((i)) (2pi), i = 0, 1, 2, where p is an element of (Graphics) and f is singular at t = 0, t = 1 and u = 0. Under suitable weaker conditions than those of [1], it is proved by constructing a special cone in C[0, 2pi] and employing the fixed point index theory that the problem has at least one or at least two positive solutions. 展开更多
关键词 singular boundary value problem third-order differential system positive solution
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THE SINGULARLY PERTURBED BOUNDARY VALUE PROBLEMS FOR HIGHER ORDER SEMILINEAR ELLIPTIC EQUATIONS 认领 引用 被引量：7
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作者 莫嘉琪 许玉兴 《Acta Mathematica Scientia》 SCIE 1997年第1期44-50,共7页
In this paper a singular perturbation of boundary value problem for elliptic partial differential equations of higher order is considered by using the differential inequalities. The uniformly valid asymptotic expansio... In this paper a singular perturbation of boundary value problem for elliptic partial differential equations of higher order is considered by using the differential inequalities. The uniformly valid asymptotic expansion in entire region is obtained. 展开更多
关键词 differential inequality singular perturbation asymptotic expansion elliptic partial differential equation boundary value problem
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EXISTENCE OF SOLUTIONS FOR HIGHER ORDER MULTI-POINT BOUNDARY VALUE PROBLEM AT RESONANCE 认领 引用 被引量：3
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作者 林晓洁 杜增吉 葛渭高 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2006年第5期705-711,共7页
Using the theory of coincidence degree, a class of higher order multi-point boundary value problem for ordinary differential equations are studied. Under the boundary conditions satisfying the resonance case, some new... Using the theory of coincidence degree, a class of higher order multi-point boundary value problem for ordinary differential equations are studied. Under the boundary conditions satisfying the resonance case, some new existence results are obtained by supposing some conditions to the nonlinear term and applying a priori estimates. 展开更多
关键词 boundary value problem resonance coincidence degree theory
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ON RIEMANN BOUNDARY VALUE PROBLEM FOR POLYANALYTIC FUNCTIONS ON THE REAL AXIS 认领 引用 被引量：11
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作者 汪玉峰 杜金元 《Acta Mathematica Scientia》 SCIE 2004年第4期663-671,共9页
In this article, Riemann boundary value problem with different factors for polyanalytic functions on the real axis is studied. The expression of solution and sufficient and necessary condition for solvability of the n... In this article, Riemann boundary value problem with different factors for polyanalytic functions on the real axis is studied. The expression of solution and sufficient and necessary condition for solvability of the non-homogeneous Riemann boundary value problem are obtained. 展开更多
关键词 Polyanalytic function Riemann boundary value problem
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RIEMANN BOUNDARY VALUE PROBLEM WITH RESPECT TO THE PERTURBATION OF BOUNDARY CURVE TO BE AN OPEN ARC 认领 引用 被引量：5
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作者 林娟 王传荣 《Acta Mathematica Scientia》 SCIE 2009年第5期1481-1488,共8页
By dint of the stability of Cauchy-type integral with kernel density of class H＊ for an open arc, this paper discusses the stability of the solution of Riemann boundary value problem with respect to the perturbation ... By dint of the stability of Cauchy-type integral with kernel density of class H＊ for an open arc, this paper discusses the stability of the solution of Riemann boundary value problem with respect to the perturbation of boundary curve to be an open arc. 展开更多
关键词 open arc Riemann boundary value problem smooth perturbation stability
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EXISTENCE OF POSITIVE SOLUTIONS FOR p-LAPLACIAN SINGULAR BOUNDARY VALUE PROBLEMS OF FUNCTIONAL DIFFERENTIAL EQUATION 认领 引用 被引量：6
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作者 SongChangxiu WengPeixuan 《Applied Mathematics(A Journal of Chinese Universities)》 2005年第1期51-58,共8页
In this paper,the boundary value problems of p-Laplacian functional differential equation are studied.By using a fixed point theorem in cones,some criteria for the existence of positive solutions are given.
关键词 p-Laplacian operator functional differential equation boundary value problem positive solution fixed point theorem in cones.
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Existence Results of Third Order Multi-Point Boundary Value Problem at Resonance 认领 引用 被引量：3
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作者 杜增吉 白占兵 葛渭高 《Journal of Beijing Institute of Technology》 EI CAS 2005年第4期449-452,共4页
A kind of third order multi-point boundary value problems, x＇＇＇（ ι） = f（ t, x （ t ）, x＂ （ t ）, x＇＇＇ （ t ） ） ＋ m 2 e（t）,t∈（0, 1）,x（0）=ax（ξ）,x＇（0）-0,x（l）= ^m2∑j=1 βjx（ηj）, fεC[0, ... A kind of third order multi-point boundary value problems, x＇＇＇（ ι） = f（ t, x （ t ）, x＂ （ t ）, x＇＇＇ （ t ） ） ＋ m 2 e（t）,t∈（0, 1）,x（0）=ax（ξ）,x＇（0）-0,x（l）= ^m2∑j=1 βjx（ηj）, fεC[0, 1]×R^3, e（t）∈L^1[0, 1],a≥0, is considered, all theβj＇s have not the same sign, 0〈ξ〈 l, 0〈η1〈 η2〈… 〈ηm.2〈 1. By using the coincidence degree theory, some existence theorems for the problems at resonance are obtained. 展开更多
关键词 multi-point boundary value problem resonance coincidence degree theory
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Periodic boundary value problem for the first order functional differential equations with impulses 认领 引用 被引量：5
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作者 LIANG Rui-xi SHEN Jian-hua 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE 2009年第1期27-35,共9页
This paper is concerned with the existence and approximation of solutions for a class of first order impulsive functional differential equations with periodic boundary value conditions. A new comparison result is pres... This paper is concerned with the existence and approximation of solutions for a class of first order impulsive functional differential equations with periodic boundary value conditions. A new comparison result is presented and the previous results are extended. 展开更多
关键词 functional differential equation periodic boundary value problem lower and upper solution monotone iterative method
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A simultaneous space-time wavelet method for nonlinear initial boundary value problems 认领 引用 被引量：2
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作者 Jizeng WANG Lei ZHANG Youhe ZHOU 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI CSCD 2018年第11期1547-1566,共20页
A high-precision and space-time fully decoupled numerical method is developed for a class of nonlinear initial boundary value problems. It is established based on a proposed Coiflet-based approximation scheme with an ... A high-precision and space-time fully decoupled numerical method is developed for a class of nonlinear initial boundary value problems. It is established based on a proposed Coiflet-based approximation scheme with an adjustable high order for the functions over a bounded interval, which allows the expansion coefficients to be explicitly expressed by the function values at a series of single points. When the solution method is used, the nonlinear initial boundary value problems are first spatially discretized into a series of nonlinear initial value problems by combining the proposed wavelet approximation and the conventional Galerkin method, and a novel high-order step-by-step time integrating approach is then developed for the resulting nonlinear initial value problems with the same function approximation scheme based on the wavelet theory. The solution method is shown to have the N th-order accuracy, as long as the Coiflet with [0, 3 N-1]compact support is adopted, where N can be any positive even number. Typical examples in mechanics are considered to justify the accuracy and efficiency of the method. 展开更多
关键词 nonlinear initial boundary value problem Coiflet numerical method
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EXISTENCE AND UNIQUENESS RESULTS FOR BOUNDARY VALUE PROBLEMS OF HIGHER ORDER FRACTIONAL INTEGRO-DIFFERENTIAL EQUATIONS INVOLVING GRONWALL'S INEQUALITY IN BANACH SPACES 认领 引用 被引量：3
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作者 Dimplekumar N.CHALISHAJAR K.KARTHIKEYAN 《Acta Mathematica Scientia》 SCIE CSCD 2013年第3期758-772,共15页
We study boundary value problems for fractional integro-differential equations involving Caputo derivative of orderα∈(n-1,n)in Banach spaces.Existence and uniqueness results of solutions are established by virtue of... We study boundary value problems for fractional integro-differential equations involving Caputo derivative of orderα∈(n-1,n)in Banach spaces.Existence and uniqueness results of solutions are established by virtue of the Holder's inequality,a suitable singular Cronwall's inequality and fixed point theorem via a priori estimate method.At last,examples are given to illustrate the results. 展开更多
关键词 Boundary value problems fractional order integro-differential equations bound-ary value problems existence and uniqueness singular gronwall inequality fixed point theorem
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CAUCHY TYPE INTEGRALS AND A BOUNDARY VALUE PROBLEM IN A COMPLEX CLIFFORD ANALYSIS 认领 引用 被引量：1
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作者 曹南斌 李尊凤 +1 位作者 杨贺菊 乔玉英 《Acta Mathematica Scientia》 SCIE CSCD 2024年第1期369-385,共17页
Clifford analysis is an important branch of modern analysis;it has a very important theoretical significance and application value,and its conclusions can be applied to the Maxwell equation,Yang-Mill field theory,quan... Clifford analysis is an important branch of modern analysis;it has a very important theoretical significance and application value,and its conclusions can be applied to the Maxwell equation,Yang-Mill field theory,quantum mechanics and value problems.In this paper,we first give the definition of a quasi-Cauchy type integral in complex Clifford analysis,and get the Plemelj formula for it.Second,we discuss the H?lder continuity for the Cauchy-type integral operators with values in a complex Clifford algebra.Finally,we prove the existence of solutions for a class of linear boundary value problems and give the integral representation for the solution. 展开更多
关键词 Clifford analysis Cauchy type integral Plemelj formula Holder continuous boundary value problems
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ON SOLUTION OF A KIND OF RIEMANN BOUNDARY VALUE PROBLEM WITH SQUARE ROOTS 认领 引用 被引量：23
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作者 Lu Jianke 《Acta Mathematica Scientia》 SCIE 2002年第2期145-149,共5页
Solution of the Riemann boundary value problem with square roots(1.1)for analytic functions proposed in[1]is reconsidered,which was solved under certain assumptions on the branch points appeared.Here the work is conti... Solution of the Riemann boundary value problem with square roots(1.1)for analytic functions proposed in[1]is reconsidered,which was solved under certain assumptions on the branch points appeared.Here the work is continued without these assumptions and the problem is solved in the general case. 展开更多
关键词 Riemann boundary value problem branch points index order at infinity sectionally holomorphic functions
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TWO POSITIVE SOLUTIONS TO THREE-POINT SINGULAR BOUNDARY VALUE PROBLEMS 认领 引用 被引量：3
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作者 李宇华 梁占平 《Acta Mathematica Scientia》 SCIE CSCD 2011年第1期29-38,共10页
In this article, we consider the existence of two positive solutions to nonlinear second order three-point singular boundary value problem： -u′′（t） = λf（t, u（t）） for all t ∈ （0, 1） subjecting to u（0） = ... In this article, we consider the existence of two positive solutions to nonlinear second order three-point singular boundary value problem： -u′′（t） = λf（t, u（t）） for all t ∈ （0, 1） subjecting to u（0） = 0 and αu（η） = u（1）, where η ∈ （0, 1）, α ∈ [0, 1）, and λ is a positive parameter. The nonlinear term f（t, u） is nonnegative, and may be singular at t = 0, t = 1, and u = 0. By the fixed point index theory and approximation method, we establish that there exists λ＊ ∈ （0, ＋∞], such that the above problem has at least two positive solutions for any λ ∈ （0, λ＊） under certain conditions on the nonlinear term f. 展开更多
关键词 Three-point singular boundary value problem positive solutions fixed point index
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Generalized variational principles for boundary value problem of electromagnetic field in electrodynamics 认领 引用 被引量：1
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作者 Cheng-bo ZHENG Bin LIU +1 位作者 Zuo-jun WANG Shi-ke ZHENG 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2010年第4期471-480,共10页
An expression of the generalized principle of virtual work for the boundary value problem of the linear and anisotropic electromagnetic field is given.Using Chien's method,a pair of generalized variational princip... An expression of the generalized principle of virtual work for the boundary value problem of the linear and anisotropic electromagnetic field is given.Using Chien's method,a pair of generalized variational principles(GVPs)are established,which directly leads to all four Maxwell's equations,two intensity-potential equations,two constitutive equations,and eight boundary conditions.A family of constrained variational principles is derived sequentially.As additional verifications,two degenerated forms are obtained,equivalent to two known variational principles.Two modified GVPs are given to provide the hybrid finite element models for the present problem. 展开更多
关键词 generalized variational principle(GVP) electromagnetic field electrodynamics boundary value problem finite element method
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