Results 1 to 10 of about 21,392,187 (250)
Elliptic problem driven by different types of nonlinearities
Boundary Value Problems, 2021 In this paper we establish the existence and multiplicity of nontrivial solutions to the following problem: ( − Δ ) 1 2 u + u + ( ln | ⋅ | ∗ | u | 2 ) = f ( u ) + μ | u | − γ − 1 u , in R , $$\begin{aligned} \begin{aligned} (-\Delta )^{\frac{1}{2}}u+u ...
Debajyoti Choudhuri, Dušan D. Repovš
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Ground State Solution for an Autonomous Nonlinear Schrödinger System
Journal of Function Spaces, 2021 In this paper, we study the following autonomous nonlinear Schrödinger system (discussed in the paper), where λ,μ, and ν are positive parameters; 2∗=2N/N−2 is the critical Sobolev exponent; and f satisfies general subcritical growth conditions.
Min Liu, Jiu Liu
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Ground state solution for fractional problem with critical combined nonlinearities
Electronic Journal of Qualitative Theory of Differential Equations, 2023 This paper is concerned with the following nonlocal problem with combined critical nonlinearities $$ (-\Delta)^{s} u=-\alpha|u|^{q-2} u+\beta{u}+\gamma|u|^{2_{s}^{*}-2}u \quad \text{in}~\Omega, \quad \quad u=0 \quad \text{in}~\mathbb{R}^{N} \backslash \
Er-Wei Xu, Hong-Rui Sun
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Ground state solution of semilinear Schrödinger system with local super-quadratic conditions
Electronic Journal of Qualitative Theory of Differential Equations, 2021 In this paper, we dedicate to studying the following semilinear Schrödinger system \begin{equation*} \begin{cases} -\Delta u+V_1(x)u =F_{u}(x,u,v)&\mbox{in}~\mathbb{R}^N, \\ -\Delta v+V_2(x)v=F_{v}(x,u,v)&\mbox{in}~\mathbb{R}^N, \\
Jing Chen, Yiqing Li
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On Kirchhoff-Type Equations with Hardy Potential and Berestycki–Lions Conditions
Mathematics, 2023 The purpose of this paper is to investigate the existence and asymptotic properties of solutions to a Kirchhoff-type equation with Hardy potential and Berestycki–Lions conditions.
Hua Yang, Jiu Liu
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Existence of Positive Ground State Solutions for Choquard Systems
Advanced Nonlinear Studies, 2020 We study the existence of positive ground state solution for Choquard systems. In the autonomous case, we prove the existence of at least one positive ground state solution by the Pohozaev manifold method and symmetric-decreasing rearrangement arguments.
Deng Yinbin, Jin Qingfei, Shuai Wei
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Positive solutions of Schrödinger-Kirchhoff-Poisson system without compact condition
Boundary Value Problems, 2017 Purpose The existence of positive solutions for a class of nonlinear Schrödinger-Kirchhoff-Poisson systems. Methods Variational method. Results Some results on the existence of positive solutions.
Fengxia Liu, Shuli Wang
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Boundary Value Problems, 2020 In this paper, we consider the existence of a least energy nodal solution and a ground state solution, energy doubling property and asymptotic behavior of solutions of the following critical problem: { − ( a + b ∫ R 3 | ∇ u | 2 d x ) Δ u + V ( x ) u + λ ...
Chungen Liu, Hua-Bo Zhang
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Ground states for a coupled Schrödinger system with general nonlinearities
Boundary Value Problems, 2020 We study a coupled Schrödinger system with general nonlinearities. By using variational methods, we prove the existence and asymptotic behaviour of ground state solution for the system with periodic couplings.
Xueliang Duan, Gongming Wei, Haitao Yang
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Ground state sign-changing solutions for Kirchhoff equations with logarithmic nonlinearity
Electronic Journal of Qualitative Theory of Differential Equations, 2019 In this paper, we study Kirchhoff equations with logarithmic nonlinearity: \begin{equation*} \begin{cases} -(a+b\int_\Omega|\nabla u|^2)\Delta u+ V(x)u=|u|^{p-2}u\ln u^2, & \mbox{in}\ \Omega,\\ u=0,& \mbox{on}\ \partial\Omega, \end{cases} \end{equation*}
Lixi Wen, Xianhua Tang, Sitong Chen
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