Advanced Nonlinear Studies, 2021 The main purpose of this paper is to establish the existence of ground-state solutions to a class of Schrödinger equations with critical exponential growth involving the nonnegative, possibly degenerate, potential V:
Chen Lu, Lu Guozhen, Zhu Maochun
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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 ...
Min Liu, Zhijing Wang, Zhenyu Guo
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Ground state solutions and infinitely many solutions for a nonlinear Choquard equation [PDF]
Boundary Value Problems, 2021 In this paper we study the existence and multiplicity of solutions for the following nonlinear Choquard equation: − Δ u + V ( x ) u = [ | x | − μ ∗ | u | p ] | u | p − 2 u , x ∈ R N , $$\begin{aligned} -\Delta u+V(x)u=\bigl[ \vert x \vert ^{-\mu }\ast ...
Tianfang Wang, Wen Zhang
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Existence and Asymptotic Behavior of Ground State Solutions to Kirchhoff-Type Equations of General Convolution Nonlinearity with a Steep Potential Well [PDF]
Mathematics, 2022 In this paper, we consider a new kind of Kirchhoff-type equation which is stated in the introduction. Under certain assumptions on potentials, we prove by variational methods that the equation has at least a ground state solution and investigate the ...
Li Zhou, Chuanxi Zhu
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Ground state solutions of inhomogeneous Bethe equations [PDF]
SciPost Physics, 2018 The distribution of Bethe roots, solution of the inhomogeneous Bethe equations, which characterize the ground state of the periodic XXX Heisenberg spin-$\frac{1}{2}$ chain is investigated.
S. Belliard, A. Faribault
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Ground state solutions for fractional p-Kirchhoff equation
Electronic Journal of Differential Equations, 2022 We study the fractional p-Kirchhoff equation $$ \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 Solutions for Kirchhoff Type Quasilinear Equations
Advanced Nonlinear Studies, 2019 In this paper, we are concerned with quasilinear equations of Kirchhoff type, and prove the existence of ground state signed solutions and sign-changing solutions by using the Nehari method.
Liu Xiangqing, Zhao Junfang
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Ground state solutions of scalar field fractional Schrödinger equations [PDF]
Calculus of Variations and Partial Differential Equations, 2015 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Giovanni Molica Bisci +1 more
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Ground state solutions of the complex Gross Pitaevskii equation associated to exciton-polariton Bose-Einstein condensates [PDF]
Journal des Mathématiques Pures et Appliquées, 2021 We investigate the existence of ground state solutions of a Gross-Pitaevskii equation modeling the dynamics of pumped Bose Einstein condensates (BEC).
Hichem Hajaiej +2 more
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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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