Results 1 to 10 of about 2,058,902 (173)

Ground state solution of a nonlocal boundary-value problem

Electronic Journal of Differential Equations, 2013
In this article, we apply the Nehari manifold method to study the Kirchhoff type equation $$ -\Big(a+b\int_\Omega|\nabla u|^2dx\Big)\Delta u=f(x,u) $$ subject to Dirichlet boundary conditions.
Cyril Joel Batkam
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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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Existence of a ground-state solution for a quasilinear Schrödinger system [PDF]

Frontiers in Physics
In this paper, we consider the following quasilinear Schrödinger system.−Δu+u+k2Δ|u|2u=2αα+β|u|α−2u|v|β,x∈RN,−Δv+v+k2Δ|v|2v=2βα+β|u|α|v|β−2v,x∈RN,where k < 0 is a real constant, α > 1, β > 1, and α + β < 2*.
Xue Zhang, Jing Zhang, Jing Zhang, Jing Zhang   +3 more
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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 solutions for fractional Kirchhoff type equations with critical growth

Electronic Journal of Differential Equations
Kexue Li
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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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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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Positive ground state solutions for a class of fractional coupled Choquard systems

AIMS Mathematics, 2023
In this paper, we combine the critical point theory and variational method to investigate the following a class of coupled fractional systems of Choquard type $ \begin{equation*} \left\{ \begin{array}{l} (-\Delta)^{s}u+\lambda_{1}u& = (I_ ...
Kexin Ouyang , Yu Wei , Huiqin Lu
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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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