Ground state sign-changing solutions for critical Choquard equations with steep well potential [PDF]
Electronic Journal of Qualitative Theory of Differential Equations, 2022 In this paper, we study sign-changing solution of the Choquard type equation \begin{align*} -\Delta u+\left(\lambda V(x)+1\right)u =\big(I_\alpha\ast|u|^{2_\alpha^*}\big)|u|^{2_\alpha^*-2}u +\mu|u|^{p-2}u\quad \mbox{in}\ \mathbb{R}^N, \end{align*} where
Yong-Yong Li, Gui-Dong Li, Chun-Lei Tang
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Infinitely Many Solutions for a Semilinear Elliptic Equation with Sign-Changing Potential [PDF]
Boundary Value Problems, 2009 We consider a similinear elliptic equation with sign-changing potential −Δu−V(x)u=f(x,u), u∈H1(ℝN), where V(x) is a function possibly changing sign in ℝN.
Li Yongqing, Chen Yu
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Infinitely many solutions for quasilinear Schrödinger equation with general superlinear nonlinearity
Boundary Value Problems, 2023 In this article, we study the quasilinear Schrödinger equation − △ ( u ) + V ( x ) u − △ ( u 2 ) u = g ( x , u ) , x ∈ R N , $$ -\triangle (u)+V(x)u-\triangle \bigl(u^{2}\bigr)u=g(x,u), \quad x\in \mathbb{R}^{N}, $$ where the potential V ( x ) $V(x)$ and
Jiameng Li +3 more
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On the existence and multiplicity of solutions for nonlinear Klein–Gordon–Maxwell system
Electronic Journal of Qualitative Theory of Differential Equations, 2023 In this paper, we study the existence and multiplicity solutions for the following Klein–Gordon–Maxwell system \begin{align*} \begin{cases} - \Delta u +V(x)u-(2\omega+\phi)\phi u =f(x,u), &x\in \mathbb{R}^3,\\ \Delta \phi =(\omega+\phi)u^2, \quad &
Lixia Wang +2 more
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Nontrivial solutions for Klein–Gordon–Maxwell systems with sign-changing potentials
Boundary Value Problems, 2022 This paper is concerned with the nonlinear Klein–Gordon–Maxwell systems. Unlike all known results in the literature, the Schrödinger operator − Δ + V $-\Delta +V$ is allowed to be indefinite and the weaker superlinear conditions are imposed instead of ...
Xian Zhang, Chen Huang
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On a class of superlinear nonlocal fractional problems without Ambrosetti–Rabinowitz type conditions
Electronic Journal of Qualitative Theory of Differential Equations, 2019 In this note, we deal with the existence of infinitely many solutions for a problem driven by nonlocal integro-differential operators with homogeneous Dirichlet boundary conditions \begin{equation*} \begin{cases} -\mathcal{L}_{K}u=\lambda f(x,u), &
Qing-Mei Zhou
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On nontrivial solutions of nonlinear Schrödinger equations with sign-changing potential
Advances in Difference Equations, 2021 In this paper, we consider the superlinear Schrödinger equation with bounded potential well. The potential here is allowed to be sign-changing. Without assuming the Ambrosetti–Rabinowitz-type condition, we prove the existence of a nontrivial solution and
Wei Chen, Yue Wu, Seongtae Jhang
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High energy solutions of modified quasilinear fourth-order elliptic equation
Boundary Value Problems, 2018 This paper focuses on the following modified quasilinear fourth-order elliptic equation: {△2u−(a+b∫R3|∇u|2dx)△u+λV(x)u−12△(u2)u=f(x,u),in R3,u(x)∈H2(R3), $$\textstyle\begin{cases} \triangle^{2}u-(a+b\int_{\mathbb{R}^{3}} \vert \nabla u \vert ^{2}\,dx ...
Xiujuan Wang, Anmin Mao, Aixia Qian
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Infinitely many weak solutions for $p(x)$-Laplacian-like problems with sign-changing potential
Electronic Journal of Qualitative Theory of Differential Equations, 2020 This study is concerned with the $p(x)$-Laplacian-like problems and arising from capillarity phenomena of the following type $$\begin{cases} -{\rm{div}}\left(\left(1+\tfrac{|\nabla u|^{p(x)}}{\sqrt{1+|\nabla u|^{2p(x)}}}\right)|\nabla u|^{p(x)-2}\nabla ...
Qing-Mei Zhou, Ke-Qi Wang
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Nonradial solutions for semilinear Schrödinger equations with sign-changing potential
Electronic Journal of Qualitative Theory of Differential Equations, 2015 In this paper, we investigate the existence of infinite nonradial solutions for the Schrödinger equations \begin{equation*} \begin{cases} -\triangle u+b(|x|)u=f(|x|, u), &\quad x\in {\mathbb{R}}^{N},\\ u\in H^{1}({\mathbb{R}}^{N}), \end ...
Dingyang Lv, Xuxin Yang
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