Results 1 to 10 of about 2,058,787 (289)

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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Solution-synthesized stable triaza[4]triangulene triradical with a quartet ground state [PDF]

Nature Communications
As 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, Di Zhang, Yushuang Zhang, Yihan Wang, Yanning Cheng, Yi Xie, Ziqi Zhu, Shang-Da Jiang, Dahui Zhao   +8 more
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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, Haibo Chen, Belal Almuaalemi   +2 more
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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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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 p-Kirchhoff equation

Electronic Journal of Differential Equations, 2022
We study the fractional p-Kirchhoff equation $$ \Big( a+b \int_{\mathbb{R}^N}{\int_{\mathbb{R}^N}} \frac{|u(x)-u(y)|^p}{|x-y|^{N+ps}}\, dx\, dy\Big) (-\Delta)_p^s u-\mu|u|^{p-2}u=|u|^{q-2}u, \quad x\in\mathbb{R}^N, $$ where \((-\Delta)_p^s\) is the fractional p-Laplacian operator, a and b are strictly positive real numbers, \(s \in (0,1)\), \(1 < p ...
Lixiong Wang, Haibo Chen, Liu Yang
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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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