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Ground State Solution for an Autonomous Nonlinear Schrödinger System [PDF]
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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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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A global approach to ground state solutions
Electronic Journal of Differential Equations, 2008 We study radial solutions of semilinear Laplace equations. We try to understand all solutions of the problem, regardless of the boundary behavior. It turns out that one can study uniqueness or multiplicity properties of ground state solutions by ...
Philip Korman
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Ground state solutions for p-biharmonic equations
Electronic Journal of Differential Equations, 2017 In this article we study the p-biharmonic equation $$ \Delta_p^2u+V(x)|u|^{p-2}u=f(x,u),\quad x\in\mathbb{R}^N, $$ where $\Delta_p^2u=\Delta(|\Delta u|^{p-2}\Delta u)$ is the p-biharmonic operator.
Xiaonan Liu +2 more
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Solution-synthesized stable triaza[4]triangulene triradical with a quartet ground state [PDF]
Nature CommunicationsAs a renowned class of open-shell molecules characterized by triangular nanographenic structures and novel magnetic properties with high-spin ground states, triangulenes are attractive targets to both synthetic chemists and molecular magnet researchers ...
Xudong Bai +8 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 , $$\begin{aligned} \begin{aligned} (-\Delta )^{\frac{1}{2}}u+u ...
Debajyoti Choudhuri, Dušan D. Repovš
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Normalized Ground State Solutions for Nonautonomous Choquard Equations
Frontiers of Mathematics, 2023 In this paper, we study normalized ground state solutions for the following nonautonomous Choquard equation: $$-Δu-λu=\left(\frac{1}{|x|^μ}\ast A|u|^{p}\right)A|u|^{p-2}u,\quad \int_{\mathbb{R}^{N}}|u|^{2}dx=c,\quad u\in H^1(\mathbb{R}^N,\mathbb{R}),$$ where $c>0$, $0< ...
Luo, Huxiao, Wang, Lushun
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Ground state solution for fractional problem with critical combined nonlinearities
Electronic Journal of Qualitative Theory of Differential Equations, 2023 This paper is concerned with the following nonlocal problem with combined critical nonlinearities $$ (-\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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