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SIGN-CHANGING SOLUTIONS FOR THE NONLINEAR schrodinger-poisson system WITH CRITICAL GROWTH

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Acta Mathematica Scientia 2023年第5期43卷 2291-2308页

作者：邓引斌帅伟杨小龙 School of Mathematics and Statistics&Hubei Key Laboratory of Mathematical Sciences Central China Normal UniversityWuhan 430079China School of Mathematics and Statistics Central China Normal UniversityWuhan 430079China

In this paper,we study the following schrodinger-poisson system with critical growth:■We establish the existence of a positive ground state solution and a least energy sign-changing solution,providing that the nonlin... 详细信息

关键词： schrodinger-poisson system ground state solution sign-changing solution critical growth

Optimal Error Estimates of Compact Finite Difference Discretizations for the schrodinger-poisson system

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Communications in Computational Physics 2013年第5期13卷 1357-1388页

作者： Yong Zhang Department of Mathematical Sciences Tsinghua UniversityBeijing100084P.R.China

We study compact finite difference methods for the schrodinger-poisson equation in a bounded domain and establish their optimal error estimates under proper regularity assumptions on wave functionψand external potential V(x).The CrankNicolson compact finite difference method and the semi-implicit compact finite difference method are both of order O(h^(4)+τ^(2))in discrete l^(2),H^(1) and l^(∞) norms with mesh size h and time step τ.For the errors of compact finite difference approximation to the second derivative and poisson potential are nonlocal,thus besides the standard energy method and mathematical induction method,the key technique in analysis is to estimate the nonlocal approximation errors in discrete l^(∞) and H^(1) norm by discrete maximum principle of elliptic equation and properties of some related *** some useful inequalities are established in this ***,extensive numerical results are reported to support our error estimates of the numerical methods.

关键词： schrodinger-poisson system Crank-Nicolson scheme semi-implicit scheme compact finite difference method Gronwall inequality the maximum principle

Positive Ground State Solutions for schrodinger-poisson system with General Nonlinearity and Critical Exponent

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Journal of Partial Differential Equations 2023年第1期36卷 68-81页

作者： CHEN Qingfang LIAO Jiafeng School of Mathematics and Information China West Normal UniversityNanchong 637009China Nanchong NO.1 Middle School Nanchong 637000China College of Mathematics Education China West Normal UniversityNanchong 637009China

In this paper,we consider the following schrodinger-poisson system{-Δu+ηΦu=f(x,μ)+μ^(5),x∈Ω,-ΔФ=μ^(2),x∈Ω,μ=Φ=0,x∈■Ω,whereΩis a smooth bounded domain in R^(3),η=±1 and the continuous function f sat... 详细信息

关键词： schrodinger-poisson system Sobolev critical exponent positive ground state solu-tion Mountain pass theorem

Existence of Positive Solutions for the Nonhomogeneous schrodinger-poisson system with Strong Singularity

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Journal of Partial Differential Equations 2021年第2期34卷 186-200页

作者： LIAO Jiafeng CHEN Qingfang ZHU Lijun College of Mathematics Education China West Normal UniversityNanchong 637002China School of Mathematics and Information China West Normal UniversityNanchong 637002China

In this paper,a class of nonhomogeneous schrodinger-poisson systems with strong singularity are *** with the variational method and Nehari method,we obtain a positive solution for this system which improves the recent... 详细信息

关键词： schrodinger-poisson system strong singularity positive solution Nehari method

Infinitely many dichotomous solutions for the Schrödinger-poisson system

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Science China Mathematics 2024年第9期67卷 2049-2070页

作者： Yuke He Benniao Li Wei Long School of Mathematics and Statistics and Jiangxi Provincial Center for Applied Mathematics Jiangxi Normal UniversityNanchang 330022China

In this paper,we consider the following schrodinger-poisson system{-ε^(2)Δu+V(x)u+K(x)Φ(x)u=|u|^(p-1)u in R^(N),-ΔΦ(x)=K(x)u^(2)in RN,,where e is a small parameter,1 详细信息

In this paper,we consider the following schrodinger-poisson system{-ε^(2)Δu+V(x)u+K(x)Φ(x)u=|u|^(p-1)u in R^(N),-ΔΦ(x)=K(x)u^(2)in RN,,where e is a small parameter,1system,which are called“dichotomous solutions”,i.e.,these solutions concentrate both in a bounded domain and near infinity.

关键词： dichotomous solutions non-degeneracy schrodinger-poisson system

BOUND STATES FOR A STATIONARY NONLINEAR SCHRDINGER-poisson system WITH SIGN-CHANGING POTENTIAL IN R^3

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Acta Mathematica Scientia 2009年第4期29卷 1095-1104页

作者：蒋永生周焕松 Wuhan Institute of Physics and Mathematics Chinese Academy of Sciences P.O.Box 71010

We study the following schrodinger-poisson system where （Pλ）{-△u＋ V（x）u＋λФ（x）u^p=x∈R^3,-△Ф=u^2,lim│x│→∞Ф（x） =0,u〉0,where λ≥0 is a parameter,1 〈 p 〈＋∞, V（x） and Q（x）=1 ,***[19] proved that（Pλ）with p∈ （2, 5） has always a positive radial solution, but （Pλ） with p E （1, 2] has solution only if λ 〉 0 small enough and no any nontrivial solution if λ≥1/*** using sub-supersolution method,we prove that there exists λ0〉0 such that（Pλ）with p ∈（1＋∞）has alaways a bound state（H^1（R^3）solution for λ∈[0,λ0）and certain functions V（x）and Q（x）in L^∞（R^3）.Moreover,for every λ∈[0,λ0）,the solutions uλ of （Pλ）converges,along a subsequence,to a solution of （P0）in H^1 as λ→0

关键词： schrodinger-poisson system sub-supersolutions supercritical Sobolev expo-nent sign-changing potential bound state