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Vector Solutions for Linearly Coupled Choquard Type Equations with Lower Critical Exponents
Advances in Mathematical Physics, Volume 2020, Issue 1, 2020., 2020 The existence, nonexistence, and multiplicity of vector solutions of the linearly coupled Choquard type equations −Δu+V1xu=Iα∗uN+α/Nuα/N−1u+λv,x∈ℝN,−Δv+V2xv=Iα∗vN+α/Nvα/N−1v+λu,x∈ℝN,u,v∈H1ℝN, are proved, where α ∈ (0, N), N ≥ 3, V1(x)V2(x) ∈ L∞(ℝN) are positive functions, and Iα denotes the Riesz potential.
Huiling Wu, Jacopo Bellazzini
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Nehari-type ground state solutions for a Choquard equation with doubly critical exponents
Advances in Nonlinear Analysis, 2020 This paper deals with the following Choquard equation with a local nonlinear perturbation:
Chen Sitong, Tang Xianhua, Wei Jiuyang
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n-Kirchhoff–Choquard equations with exponential nonlinearity
Nonlinear Analysis, 2019 This article deals with the study of the following Kirchhoff equation with exponential nonlinearity of Choquard type (see $(KC)$ below). We use the variational method in the light of Moser-Trudinger inequality to show the existence of weak solutions to $(KC)$.
Arora, R. +3 more
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Advances in Nonlinear Analysis, 2020 In this paper, we study blow-up criteria and instability of normalized standing waves for the fractional Schrödinger-Choquard ...
Binhua Feng, Chen Ruipeng, Liu Jiayin
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On the Ground State to Hamiltonian Elliptic System with Choquard’s Nonlinear Term
Advances in Mathematical Physics, Volume 2020, Issue 1, 2020., 2020 In the present paper, we consider the following Hamiltonian elliptic system with Choquard’s nonlinear term −Δu+Vxu=∫ΩGvy/x−yβdygv in Ω,−Δv+Vxv=∫ΩFuy/x−yαdyfu in Ω,u=00,v= on ∂Ω,where Ω ⊂ ℝN is a bounded domain with a smooth boundary, 0 < α < N, 0 < β < N, and F is the primitive of f, similarly for G.
Wenbo Wang +3 more
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High energy solutions of the Choquard equation
Discrete & Continuous Dynamical Systems - A, 2018 The present paper is concerned with the existence of positive high energy solution of the Choquard equation. Under certain assumptions, the ground state of Choquard equation can not be achieved. However, by global compactness analysis, we prove that there exists a positive high energy solution.
Cao, Daomin, Li, Hang
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Existence of solutions for a nonlinear Choquard equation with potential vanishing at infinity
Advances in Nonlinear Analysis, 2016 We study the following nonlinear Choquard equation:
Alves Claudianor O. +2 more
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Infinitely many solutions for nonhomogeneous Choquard equations
Electronic Journal of Qualitative Theory of Differential Equations, 2019 In this paper, we study the following nonhomogeneous Choquard equation \begin{equation*} \begin{split} -\Delta u+V(x)u=(I_\alpha*|u|^p)|u|^{p-2}u+f(x),\qquad x\in \mathbb{R}^N, \end{split} \end{equation*} where $N\geq3,\alpha\in(0,N),p\in \big[\frac{N ...
Tao Wang, Hui Guo
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Existence and concentration of ground state solutions for a critical nonlocal Schr\"odinger equation in $\R^2$ [PDF]
, 2016 We study the following singularly perturbed nonlocal Schr\"{o}dinger equation $$ -\vr^2\Delta u +V(x)u =\vr^{\mu-2}\Big[\frac{1}{|x|^{\mu}}\ast F(u)\Big]f(u) \quad \mbox{in} \quad \R^2, $$ where $V(x)$ is a continuous real function on $\R^2$, $F(s)$ is ...
Alves, Claudianor O. +3 more
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Boundary Value Problems, 2020 In this paper, we study the following Choquard type quasilinear Schrödinger equation: − Δ u + u − Δ ( u 2 ) u = ( I α ∗ G ( u ) ) g ( u ) , x ∈ R N , $$ -\Delta u+u-\Delta \bigl(u^{2}\bigr)u=\bigl(I_{\alpha }*G(u) \bigr)g(u),\quad x\in {\mathbb{R}}^{N}, $
Yu-bo He, Jue-liang Zhou, Xiao-yan Lin
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