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Existence of Ground State Solutions to Nonlinear Schrödinger-Poisson System with Doping Profile and Coercive Potential 认领 引用
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作者 HAO Xiaodong HUANG Shuibo ZHANG Huanhuan 《Wuhan University Journal of Natural Sciences》 CAS CSCD 2026年第3期281-290,共10页
This paper investigates the existence of ground state solutions to the following nonlinear Schrödinger-Poisson system by variational methods{-Δu+ωu+V(x)u+eФu=|u|p-2u,x∈R3,-ΔФ=e/2(u2-ρ(x)),x∈R3... This paper investigates the existence of ground state solutions to the following nonlinear Schrödinger-Poisson system by variational methods{-Δu+ωu+V(x)u+eФu=|u|p-2u,x∈R3,-ΔФ=e/2(u2-ρ(x)),x∈R3,provided that ρ(x)≥0 and e2‖ρ‖6/5≤ρ0with ρ0>0 small enough,where 40 denotes a coupling constant,ω>0 is a Lagrange multiplier,the potential V(x)is coercive and the doping profile ρ(x)satisfies appropriate decay conditions.The introduction of ρ(x)compromises the coercivity of the energy functional.Therefore,we establish the existence of ground state solutions by considering the minimization problem on Nehari manifold. 展开更多
关键词 doping profile ground state solution Nehari manifold variational methods
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Normalized Positive Ground State Solutions for Nonhomogeneous Kirchhoff Equations 认领 引用
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作者 ZHANG Xiaocang XU Liping 《应用数学》 北大核心 2025年第3期711-720,共10页
This article studies a class of nonlinear Kirchhoff equations with exponential critical growth,trapping potential,and perturbation.Under appropriate assumptions about f and h,the article obtained the existence of norm... This article studies a class of nonlinear Kirchhoff equations with exponential critical growth,trapping potential,and perturbation.Under appropriate assumptions about f and h,the article obtained the existence of normalized positive solutions for this equation via the Trudinger-Moser inequality and variational methods.Moreover,these solutions are also ground state solutions.Additionally,the article also characterized the asymptotic behavior of solutions.The results of this article expand the research of relevant literature. 展开更多
关键词 Normalized positive ground state solution Nonhomogeneous Kirchhoff equation Variational method Exponential critical growth Trapping potential
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POSITIVE GROUND STATE SOLUTIONS FOR A QUASILINEAR SCHRODINGER EQUATION 认领 引用
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作者 JIN Qing-fei 《数学杂志》 2025年第2期95-110,共16页
This paper is concerned with the positive ground state solutions for a quasilinear Schrodinger equation with a Hardy-type term.We obtain positive ground state solutions for the given quasilinear Schrodinger equation b... This paper is concerned with the positive ground state solutions for a quasilinear Schrodinger equation with a Hardy-type term.We obtain positive ground state solutions for the given quasilinear Schrodinger equation by using a change of variables and variational method. 展开更多
关键词 Quasilinear equation schrodinger equation positive ground state solutions variational methods
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EXISTENCE AND CONCENTRATION BEHAVIOR OF GROUND STATE SOLUTIONS FOR A CLASS OF GENERALIZED QUASILINEAR SCHRODINGER EQUATIONS IN R^N 认领 引用 被引量：2
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作者 Jianhua CHEN Xianjiu HUANG +1 位作者 Bitao CHENG Xianhua TANG 《Acta Mathematica Scientia》 SCIE CSCD 2020年第5期1495-1524,共30页
In this article,we study the generalized quasilinear Schrodinger equation-div(ε^2g^2(u)▽u)+ε^2g(u)g′(u)|▽u|^2+V(x)u=K(x)|u|^p-2u,x∈R^N where A≥3,e>0,4<p<,22*,g∈C 1(R,R+),V∈C(R^N)∩L∞(R^N)has a posit... In this article,we study the generalized quasilinear Schrodinger equation-div(ε^2g^2(u)▽u)+ε^2g(u)g′(u)|▽u|^2+V(x)u=K(x)|u|^p-2u,x∈R^N where A≥3,e>0,4<p<,22*,g∈C 1(R,R+),V∈C(R^N)∩L∞(R^N)has a positive global minimum,and K∈C(R^N)∩L∞(R^N)has a positive global maximum.By using a change of variable,we obtain the existence and concentration behavior of ground state solutions for this problem and establish a phenomenon of exponential decay. 展开更多
关键词 generalized quasilinear Schrodinger equation ground state solutions existence concentration behavior
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GROUND STATE SOLUTIONS OF NEHARI-POHOZAEV TYPE FOR A FR ACTIONAL SCHRODINGER-POISSON SYSTEM WITH CRITICAL GROWTH 认领 引用 被引量：2
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作者 Wentao HUANG Li WANG 《Acta Mathematica Scientia》 SCIE CSCD 2020年第4期1064-1080,共17页
We study the following nonlinear fractional Schrodinger-Poisson system with critical growth:{(-△)sμ+μ+φμ=f(μ)+|μ|2s-2μ,x∈R3.(-△)tφ=μ2x∈R3,(0.1)where 03 and 2s=6/3-2s is the critical Sobolev exponent in 1R... We study the following nonlinear fractional Schrodinger-Poisson system with critical growth:{(-△)sμ+μ+φμ=f(μ)+|μ|2s-2μ,x∈R3.(-△)tφ=μ2x∈R3,(0.1)where 03 and 2s=6/3-2s is the critical Sobolev exponent in 1R3.Under some more general assumptions on f,we prove that(0.1)admits a nontrivial ground state solution by using a constrained minimization on a Nehari-Pohozaev manifold. 展开更多
关键词 fractional Schrodinger-Poisson system Nehari-Pohozaev manifold ground state solutions critical growth
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ON GROUND STATE SOLUTIONS FOR SUPERLINEAR DIRAC EQUATION 认领 引用 被引量：1
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作者 张健 唐先华 张文 《Acta Mathematica Scientia》 SCIE CSCD 2014年第3期840-850,共11页
This article is concerned with the nonlinear Dirac equations-iδtψ=ich ∑k=1^3 αkδkψ-mc^2βψ＋Rψ（x,ψ） in R^3.Under suitable assumptions on the nonlinearity, we establish the existence of ground state solution... This article is concerned with the nonlinear Dirac equations-iδtψ=ich ∑k=1^3 αkδkψ-mc^2βψ＋Rψ（x,ψ） in R^3.Under suitable assumptions on the nonlinearity, we establish the existence of ground state solutions by the generalized Nehari manifold method developed recently by Szulkin and Weth. 展开更多
关键词 Nonlinear Dirac equation ground state solutions generalized Nehari manifold strongly indefinite functionals
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THE EXISTENCE AND CONCENTRATION OF GROUND STATE SOLUTIONS FOR CHERN-SIMONS-SCHR?DINGER SYSTEMS WITH A STEEP WELL POTENTIAL 认领 引用 被引量：4
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作者 Jinlan TAN Yongyong LI Chunlei TANG 《Acta Mathematica Scientia》 SCIE CSCD 2022年第3期1125-1140,共16页
In this paper,we investigate a class of nonlinear Chern-Simons-Schr?dinger systems with a steep well potential.By using variational methods,the mountain pass theorem and Nehari manifold methods,we prove the existence ... In this paper,we investigate a class of nonlinear Chern-Simons-Schr?dinger systems with a steep well potential.By using variational methods,the mountain pass theorem and Nehari manifold methods,we prove the existence of a ground state solution forλ>0 large enough.Furthermore,we verify the asymptotic behavior of ground state solutions asλ→+∞. 展开更多
关键词 Chern-Simons-Schrödinger system steep well potential ground state solution concentration
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GROUND STATE SOLUTIONS FOR A SCHRODINGER-POISSON SYSTEM WITH UNCONV ENTIONAL POTENTIAL 认领 引用 被引量：2
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作者 Yao DU Chuniei TANG 《Acta Mathematica Scientia》 SCIE CSCD 2020年第4期934-944,共11页
We consider the Schrodinger-Poisson system with nonlinear term Q(x)|u|^p-1u,where the value of |x|→∞ lim Q(x)may not exist and Q may change sign.This means that the problem may have no limit problem.The existence of... We consider the Schrodinger-Poisson system with nonlinear term Q(x)|u|^p-1u,where the value of |x|→∞ lim Q(x)may not exist and Q may change sign.This means that the problem may have no limit problem.The existence of nonnegative ground state solutions is established.Our method relies upon the variational method and some analysis tricks. 展开更多
关键词 Schrodinger-Poisson system ground state solutions no limit problem
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EXISTENCE OF A GROUND STATE SOLUTION FOR THE CHOQUARD EQUATION WITH NONPERIODIC POTENTIALS 认领 引用
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作者 罗缘圆 高冬梅 王俊 《Acta Mathematica Scientia》 SCIE CSCD 2023年第1期303-323,共21页
We study the Choquard equation-Δu+V(x)u-b(x)∫R3|u(y)|2/|x-y|dyu,x∈R3,where V(x)=V1(x),b(x)=b1(x)for x1>0 and V(x)=V2(x),b(x)=b2(x)for x1<0,and V1,V2,b1and b2are periodic in each coordinate direction.Under som... We study the Choquard equation-Δu+V(x)u-b(x)∫R3|u(y)|2/|x-y|dyu,x∈R3,where V(x)=V1(x),b(x)=b1(x)for x1>0 and V(x)=V2(x),b(x)=b2(x)for x1<0,and V1,V2,b1and b2are periodic in each coordinate direction.Under some suitable assumptions,we prove the existence of a ground state solution of the equation.Additionally,we find some sufficient conditions to guarantee the existence and nonexistence of a ground state solution of the equation. 展开更多
关键词 Choquard equation ground state solution critical points variational methods
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A GROUND STATE SOLUTION TO THE CHERN-SIMONS-SCHRODINGER SYSTEM 认领 引用
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作者 Jin DENG Benniao LI 《Acta Mathematica Scientia》 SCIE CSCD 2022年第5期1743-1764,共22页
In this paper,we consider the Chern-Simons-Schrodinger system{−Δu+[e2|A|2+(V(x)+2eA0)+2(1+κq/2)N]u+q|u|p−2u=0,−ΔN+κ2q2N+q(1+κq2)u2=0,κ(∂1A2−∂2A1)=−eu2,∂1A1+∂2A2=0,... In this paper,we consider the Chern-Simons-Schrodinger system{−Δu+[e2|A|2+(V(x)+2eA0)+2(1+κq/2)N]u+q|u|p−2u=0,−ΔN+κ2q2N+q(1+κq2)u2=0,κ(∂1A2−∂2A1)=−eu2,∂1A1+∂2A2=0,κ∂1A0=e2A2u2,κ∂2A0=−e2A1u2,where u∈H1(R2),p∈(2,4),Aα:R2→R are the components of the gauge potential(α=0,1,2),N:R2→R is a neutral scalar field,V(x)is a potential function,the parametersκ,q>0 represent the Chern-Simons coupling constant and the Maxwell coupling constant,respectively,and e>0 is the coupling constant.In this paper,the truncation function is used to deal with a neutral scalar field and a gauge field in the Chern-Simons-Schrödinger problem.The ground state solution of the problem(P)is obtained by using the variational method. 展开更多
关键词 Chern-Simons-Schrodinger systems ground state solution variational method
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Classification of Positive Ground State Solutions with Different Morse Indices for Nonlinear N-Coupled Schrödinger System 认领 引用
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作者 Juncheng Wei Maoding Zhen 《Analysis in Theory and Applications》 CSCD 2021年第2期230-266,共37页
In this paper,we study the following N-coupled nonlinear Schrodinger system■,wheren≤3,N≥3,uj>0,βi,j=βj,i>0 are constants andβj,j=μj,j=1,...,N.There have been intensive studies for the system on existenceo... In this paper,we study the following N-coupled nonlinear Schrodinger system■,wheren≤3,N≥3,uj>0,βi,j=βj,i>0 are constants andβj,j=μj,j=1,...,N.There have been intensive studies for the system on existenceon-existence and clas-sification of ground state solutions when N=2.However fewer results about the classification of ground state solution are available for N≥3.In this paper,we first give a complete classification result on ground state solutions with Morse indices 1,2 or 3 for three-coupled Schrodinger system.Then we generalize our results to N-coupled Schrodinger system for ground state solutions with Morse indices 1 and N.We show that any positive ground state solutions with Morse index 1 or Morse index N must be the form of(d1w,d2w,...,dNw)under suitable conditions,where w is the unique positive ground state solution of certain equation.Finally,we generalize our results to fractional N-coupled Schrödinger system. 展开更多
关键词 Nonlinear Schrödinger system unique ground state solution variational method Morse indices
Ground State Solutions for Schrdinger-Poisson Systems 认领 引用
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作者 XU Na 《Chinese Quarterly Journal of Mathematics》 2016年第1期9-18,共10页
This paper deals with a class of Schr¨odinger-Poisson systems. Under some conditions, we prove that there exists a ground state solution of the system. The proof is based on the compactness lemma for the system. ... This paper deals with a class of Schr¨odinger-Poisson systems. Under some conditions, we prove that there exists a ground state solution of the system. The proof is based on the compactness lemma for the system. Our results here improve some existing results in the literature. 展开更多
关键词 Schrdinger-Poisson system ground state solution compactness
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Normalized Ground State Solutions of Nonlinear Choquard Equations with Nonconstant Potential 认领 引用
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作者 LI Nan ZHAO Hui-yan XU Li-ping 《Chinese Quarterly Journal of Mathematics》 2024年第3期250-261,共12页
In this paper,we mainly focus on the following Choquard equation-{△u-V(x)(Ia*|u|p)|u|p-2u=λu,x∈RN,u∈H1(RN)where N≥1,λ∈R will arise as a Lagrange multiplier,0<a<N and N+a/N<p<N+a+2/... In this paper,we mainly focus on the following Choquard equation-{△u-V(x)(Ia*|u|p)|u|p-2u=λu,x∈RN,u∈H1(RN)where N≥1,λ∈R will arise as a Lagrange multiplier,0<a<N and N+a/N<p<N+a+2/N Under appropriate hypotheses on V(x),we prove that the above Choquard equation has a normalized ground state solution by utilizing variational methods. 展开更多
关键词 Choquard equation Nonconstant potential function Normalized ground state solutions Variational methods
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Ground State Solutions for a Kind of Schrödinger-Poisson System with Upper Critical Exponential Convolution Term 认领 引用
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作者 Yaolan Tang Qiongfen Zhang 《Journal of Applied Mathematics and Physics》 2022年第2期576-588,共13页
This paper mainly discusses the following equation: where the potential function V : R3 → R, α ∈ (0,3), λ > 0 is a parameter and Iα is the Riesz potential. We study a class of Schr&#246;dinger-Poisson syst... This paper mainly discusses the following equation: where the potential function V : R3 → R, α ∈ (0,3), λ > 0 is a parameter and Iα is the Riesz potential. We study a class of Schr&#246;dinger-Poisson system with convolution term for upper critical exponent. By using some new tricks and Nehair-Poho&#382;ave manifold which is presented to overcome the difficulties due to the presence of upper critical exponential convolution term, we prove that the above problem admits a ground state solution. 展开更多
关键词 Convolution Nonlinearity Schrödinger-Poisson System Upper Critical Exponent Ground State Solution
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The Existence of Ground State Solutions for Schrödinger-Kirchhoff Equations Involving the Potential without a Positive Lower Bound 认领 引用
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作者 Yuqi Wang Die Wang Shaoxiong Chen 《Journal of Applied Mathematics and Physics》 2023年第3期790-803,共14页
In this paper, we study the following Schrödinger-Kirchhoff equation where V(x) ≥ 0 and vanishes on an open set of R2 and f has critical exponential growth. By using a version of Trudinger-Moser inequality and v... In this paper, we study the following Schrödinger-Kirchhoff equation where V(x) ≥ 0 and vanishes on an open set of R2 and f has critical exponential growth. By using a version of Trudinger-Moser inequality and variational methods, we obtain the existence of ground state solutions for this problem. 展开更多
关键词 Schrödinger-Kirchhoff Equations Critical Exponential Growth Ground State Solution Degenerate Potential
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Ground State Normalized Solution for Nonhomogeneous Schrödinger-Poisson-Slater Equations with Potential 认领 引用
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作者 QIU Shuang-shuang XU Li-ping 《Chinese Quarterly Journal of Mathematics》 2026年第2期147-161,共15页
In this paper,we primarily investigate the existence of ground state normalized solutions to the following nonhomogeneous Schrödinger-Poisson-Slater equation:−Δu+λu+V(∣x∣)u+(∣x∣−1∗∣u∣2)u=g(u)+h(∣x... In this paper,we primarily investigate the existence of ground state normalized solutions to the following nonhomogeneous Schrödinger-Poisson-Slater equation:−Δu+λu+V(∣x∣)u+(∣x∣−1∗∣u∣2)u=g(u)+h(∣x∣)in R3,∫R3∣u∣2dx=m,00 is prescribed.Under suitable assumptions on V(|x|)and h(|x|),and assuming that the nonlinear term g is mass subcritical,we establish the existence of a ground state normalized solution through variational methods,thereby extending previous results in the literature. 展开更多
关键词 Nonlinear Schrödinger-Poisson-Slater equations Ground state normalized solutions Variational methods Potential Perturbation
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Positive Ground State Solutions for a Schrodinger-Newton System with Negative Critical Nonlocal Term 认领 引用
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作者 PU Yang ZHU Ljun LIAO Jiafeng 《Journal of Partial Differential Equations》 CSCD 2025年第2期171-184,共14页
We consider the following Schrodinger-Newton system with negative critical nonlocal term where a and f satisfy some certain conditions.By using the variational method and analytical techniques,we obtain the existence ... We consider the following Schrodinger-Newton system with negative critical nonlocal term where a and f satisfy some certain conditions.By using the variational method and analytical techniques,we obtain the existence of positive ground state solutions which improves the recent results in the literature. 展开更多
关键词 Schrodinger-Newton system critical nonlocal term variational method ground state solution
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Ground State Solutions to a Coupled Nonlinear Logarithmic Hartree System 认领 引用
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作者 HE Qihan LI Yafei PENG Yanfang 《Journal of Partial Differential Equations》 CSCD 2025年第1期61-79,共19页
In this paper,we study the following coupled nonlinear logarithmic Hartree system{-Δu+λ1u=μ1(-1/2πln|x|*u2)u+β(-1/2πln|x|*v2)u,x∈R2,-Δv+λ2v=μ2(-1/2πln|x|*v2)v+β(-1/2πln|x|*u2)v,... In this paper,we study the following coupled nonlinear logarithmic Hartree system{-Δu+λ1u=μ1(-1/2πln|x|*u2)u+β(-1/2πln|x|*v2)u,x∈R2,-Δv+λ2v=μ2(-1/2πln|x|*v2)v+β(-1/2πln|x|*u2)v,x∈R2,where β,μi,λi(i=1,2)are positive constants,* denotes the convolution in R2.By considering the constraint minimum problem on the Nehari manifold,we prove the existence of ground state solutions for β>0 large enough.Moreover,we also show that every positive solution is radially symmetric and decays exponentially. 展开更多
关键词 Hartree system Logarithmic convolution potential ground state solution radial symmetry
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Existence of ground state solutions of Nehari-Pankov type to Schr?dinger systems 认领 引用 被引量：1
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作者 Xianhua Tang Xiaoyan Li 《Science China Mathematics》 SCIE CSCD 2020年第1期113-134,共22页
This paper is dedicated to studying the following elliptic system of Hamiltonian type:■where N≥3,V,Q∈C(RN,R),V(x)is allowed to be sign-changing and inf Q>0,and F∈C1(R2,R)is superquadratic at both 0 and infinity... This paper is dedicated to studying the following elliptic system of Hamiltonian type:■where N≥3,V,Q∈C(RN,R),V(x)is allowed to be sign-changing and inf Q>0,and F∈C1(R2,R)is superquadratic at both 0 and infinity but subcritical.Instead of the reduction approach used in Ding et al.(2014),we develop a more direct approach—non-Nehari manifold approach to obtain stronger conclusions but under weaker assumptions than those in Ding et al.(2014).We can find anε0>0 which is determined by terms of N,V,Q and F,and then we prove the existence of a ground state solution of Nehari-Pankov type to the coupled system for allε∈(0,ε0]. 展开更多
关键词 Hamiltonian elliptic system ground state solutions of Nehari-Pankov type strongly indefinite functionals
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On the Existence of Ground State Solutions to a Quasilinear Schr?dinger Equation involving p-Laplacian 认领 引用
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作者 Ji-xiu WANG Qi GAO 《Acta Mathematicae Applicatae Sinica》 SCIE CSCD 2023年第2期381-395,共15页
We consider the following quasilinear Schrodinger equation involving p-Laplacian-Δpu+V(x)|u|p-2u-Δp(|u|2η)|u|2η-2u=λ|u|q-2u/|x|μ+|u|2ηp*(v-2)u/|x|vin RN,where N>p>1,η≥p/2(p-1),p0... We consider the following quasilinear Schrodinger equation involving p-Laplacian-Δpu+V(x)|u|p-2u-Δp(|u|2η)|u|2η-2u=λ|u|q-2u/|x|μ+|u|2ηp*(v-2)u/|x|vin RN,where N>p>1,η≥p/2(p-1),p0,μ,ν∈[0,p).Via the Mountain Pass Theorem and the Concentration Compactness Principle,we establish the existence of nontrivial ground state solutions for the above problem. 展开更多
关键词 quasilinear Schrodinger equation critical Hardy-Sobolev exponent ground state solutions singularities
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