Results 21 to 30 of about 2,064,106 (289)
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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Ground state and non-ground state solutions of some strongly coupled elliptic systems [PDF]
Transactions of the American Mathematical Society, 2011 We study an elliptic system of the formLu=|v|p−1vLu = \left | v\right |^{p-1} vandLv=|u|q−1uLv=\left | u\right |^{q-1} uinΩ\Omegawith homogeneous Dirichlet boundary condition, whereLu:=−ΔuLu:=-\Delta uin the case of a bounded domain andLu:=−Δu+uLu:=-\Delta u + uin the cases of an exterior domain or the whole spaceRN\mathbb {R}^N.
Bonheure, Denis +2 more
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Ground state solutions of inhomogeneous Bethe equations [PDF]
SciPost Physics, 2018 The distribution of Bethe roots, solution of the inhomogeneous Bethe equations, which characterize the ground state of the periodic XXX Heisenberg spin- \frac{1}{2} 1
Belliard, Samuel, Faribault, Alexandre
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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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Ground state solutions for the nonlinear Schrödinger–Maxwell equations
Journal of Mathematical Analysis and Applications, 2008 27 ...
Azzollini, A., POMPONIO, Alessio
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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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On weak interaction between a ground state and a trapping potential [PDF]
, 2014 We study the interaction of a ground state with a class of trapping potentials. We track the precise asymptotic behavior of the solution if the interaction is weak, either because the ground state moves away from the potential or is very fast.Comment: 34
Cuccagna, Scipio, Maeda, Masaya
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Ground State Solutions to a Critical Nonlocal Integrodifferential System [PDF]
Advances in Mathematical Physics, 2018 Consider the following nonlocal integrodifferential system: LKu+λ1u+μ1u2⁎-2u+Gu(x,u,v)=0 in Ω, LKv+λ2v+μ2v2⁎-2v+Gv(x,u,v)=0 in Ω, u=0, v=0 in RN∖Ω, where LK is a general nonlocal integrodifferential operator, λ1,λ2,μ1,μ2>0, 2⁎≔2N/N-2s is a fractional Sobolev critical exponent, 0<s<1, N>2s, G(x,u,v) is a lower order perturbation of ...
Min Liu, Zhijing Wang, Zhenyu Guo
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