Results 1 to 10 of about 91,560 (157)
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
doaj +3 more sources
Multiple solutions for a fractional p-Laplacian equation with sign-changing potential
Electronic Journal of Differential Equations, 2016 We use a variant of the fountain Theorem to prove the existence of infinitely many weak solutions for the fractional p-Laplace equation $$\displaylines{ (-\Delta)_p^s u + V(x) |u|^{p-2}u = f(x, u) \quad \text{in } \mathbb{R}^N, }$$ where $s\in (0,1)
Vincenzo Ambrosio
doaj +4 more sources
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
doaj +3 more sources
On nontrivial solutions of nonlinear Schrödinger equations with sign-changing potential [PDF]
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
doaj +2 more sources
On an eigenvalue problem with variable exponents and sign-changing potential
Electronic Journal of Qualitative Theory of Differential Equations, 2015 In this paper we study a non-homogeneous eigenvalue problem involving variable growth conditions and a sign-changing potential. We prove that any $\lambda>0$ sufficiently small is an eigenvalue of the nonhomogeneous eigenvalue problem \begin{equation ...
Bin Ge
doaj +2 more sources
Sign-changing solutions for p -biharmonic equations with Hardy potential
Journal of Mathematical Analysis and Applications, 2014 The paper under review is concerned with the existence of nodal solutions for a class of \(p\)-biharmonic equations with Hardy potential and Dirichlet boundary condition. By means of variational arguments, the authors establish the existence of a sign-changing solution for small positive values of the parameter.
Xiangqing Liu
exaly +2 more sources
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
doaj +2 more sources
Existence of solutions for the fractional Kirchhoff equations with sign-changing potential [PDF]
Boundary Value Problems, 2018 In this paper, the authors investigate the following fractional Kirchhoff boundary value problem: {(a+b∫0T(0Dtαu)2dt)tDTα(0Dtαu)+λV(t)u=f(t,u),t∈[0,T],u(0)=u(1)=0, $$ \textstyle\begin{cases} ( {a+b\int_{0}^{T} {({ }_{0}D_{t}^{\alpha }u)^{2}\,dt} } ){ }_ ...
Guoqing Chai, Weiming Liu
doaj +2 more sources
Discrete Dynamics in Nature and Society, 2022 In this paper, we consider the following Kirchhoff problem −a+b∫R3∇u2dxΔu+λVxu=up−2u, in R3u∈H1R3 where a,b>0 are constants, λ is a positive parameter, and ...
Guocui Yang +2 more
doaj +3 more sources
Subcritical perturbations of resonant linear problems with sign-changing potential
Electronic Journal of Differential Equations, 2005 We establish existence and multiplicity theorems for a Dirichlet boundary-value problem at resonance. This problem is a nonlinear subcritical perturbation of a linear eigenvalue problem studied by Cuesta, and includes a sign-changing potential. We obtain
Teodora-Liliana Dinu
doaj +4 more sources