Results 21 to 30 of about 2,722,864 (361)
Existence of ground state solutions for a Choquard double phase problem [PDF]
Nonlinear Analysis: Real World Applications, 2022 In this paper we study quasilinear elliptic equations driven by the double phase operator involving a Choquard term of the form \begin{align*} -\mathcal{L}_{p,q}^{a}(u) + |u|^{p-2}u+ a(x) |u|^{q-2}u = \left( \int_{\mathbb{R}^N} \frac{F(y, u)}{|x-y|^\mu}\,
Rakesh Arora +3 more
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Existence of ground state solutions to some Nonlinear Schrödinger equations on lattice graphs [PDF]
Calculus of Variations and Partial Differential Equations, 2021 In this paper, we study the nonlinear Schrödinger equation $$ -\Delta u+V(x)u=f(x,u) $$ - Δ u + V ( x ) u = f ( x , u ) on the lattice graph $$\mathbb {Z}^{N}$$ Z N .
B. Hua, Wendi Xu
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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 Solutions of Schrödinger-Kirchhoff Equations with Potentials Vanishing at Infinity
Journal of Function Spaces, 2023 In this paper, we deal with the following Schrödinger-Kirchhoff equation with potentials vanishing at infinity: −
Dongdong Sun
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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 ...
Min Liu, Jiu Liu
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On nonlinear fractional Choquard equation with indefinite potential and general nonlinearity
Boundary Value Problems, 2023 In this paper, we consider a class of fractional Choquard equations with indefinite potential ( − Δ ) α u + V ( x ) u = [ ∫ R N M ( ϵ y ) G ( u ) | x − y | μ d y ] M ( ϵ x ) g ( u ) , x ∈ R N , $$ (-\Delta )^{\alpha}u+V(x)u= \biggl[ \int _{{\mathbb{R ...
Fangfang Liao +3 more
doaj +1 more source
Ground state solutions of the non-autonomous Schrödinger–Bopp–Podolsky system
Analysis and Mathematical Physics, 2021 In this paper, we consider the following non-autonomous Schrödinger–Bopp–Podolsky system -Δu+V(x)u+q2ϕu=f(u)-Δϕ+a2Δ2ϕ=4πu2inR3.\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage ...
Sitong Chen +3 more
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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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Nonlinear bound states on weakly homogeneous spaces [PDF]
, 2012 We prove the existence of ground state solutions for a class of nonlinear elliptic equations, arising in the production of standing wave solutions to an associated family of nonlinear Schr\"odinger equations.
Christianson, Hans +3 more
core +2 more sources
Journal of Differential Equations, 2020 Consider the semilinear Schrodinger equation { − △ u + V ( x ) u = f ( x , u ) , x ∈ R N , u ∈ H 1 ( R N ) , where both V ( x ) and f ( x , u ) are periodic in x, 0 belongs to a spectral gap of − △ + V , and f ( x , u ) is subcritical and allowed to be ...
Xianhua Tang +3 more
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