Related papers: Infinitely many sign-changing solutions for the no…

This paper is concerned with the existence of sign-changing solutions to non local Kirchhoff type problems of the form \begin{equation}\label{s}\tag{S} -\Big(a+b\int_\Omega|\nabla u|^2dx\Big)\Delta u=f(x,u)\, \text{ in }\Omega,\quad\quad…

In this paper, we consider the following nonlinear Schr\"odinger system: -$\Delta$ u+P(x)u=$\mu_1$ $u^3$+$\beta$ u$v^2$, x $\in$ $R^3$,\\ -$\Delta$ v+Q(x)v=$\mu_2$ $v^3$+$\beta$ $u^2$v, x $\in$ $R^3$, where $P(x),Q(x)$ are positive radial…

In this paper, we study the existence of ground state solutions for the nonlinear fractional Schr\"{o}dinger-Poisson system \begin{equation*} \left\{ \begin{array}{ll} (-\Delta)^su+V(x)u+\phi u=|u|^{p-1}u, & \hbox{in $\mathbb{R}^3$,}…

In this work we prove the existence of infinitely many nonradial solutions that change signal to the problem $-\Delta u=f(u)$ in $B$ with $u=0$ on $\partial B$, where $B$ is the unit ball in $\mathbb{R}^2$ and $f$ is a continuous and odd…

Using variational methods we prove some results about existence and multiplicity of positive bound states of to the following Schr\"odinger-Poisson system: $$ \left\{ \begin{array}{l} \vspace{2mm} -\Delta u+V(x)u+K(x)\phi(x)u=u^5 -\Delta…

In this paper, a class of coupled systems of nonlinear Schrodinger equations with sign-changing potential, including the linearly coupled case, is considered. The existence of non-trivial bound state solutions via linking methods for cones…

In this article we study the existence of solutions to the system \begin{equation*}\left\{ \begin{array}{ll} -\left(a+b\int_{\Omega}|\nabla u|^{2}\right)\Delta u +\phi u= f(x, u) &\text{in }\Omega \hbox{} -\Delta \phi= u^{2} &\text{in…

We study the following Schr\"odinger-Poisson system (P_\lambda){ll} -\Delta u + V(x)u+\lambda \phi (x) u =Q(x)u^{p}, x\in \mathbb{R}^3 \\ -\Delta\phi = u^2, \lim\limits_{|x|\to +\infty}\phi(x)=0, u>0, where $\lambda\geqslant0$ is a…

We find a sign-changing solution for a class of Schr\"odinger-Poisson system in $\mathbb{R}^3$ as an existence result by minimization in a closed subset containing all the sign-changing solutions of the equation. The proof is based on…

In this paper we establish the existence of bound state solutions of any given order to $$ \Delta_m u +f(u)=0, x\in R^N, N\ge m>1, (P) $$ where $\Delta_m u=\nabla\cdot(|\nabla u|^{m-2}\nabla u)$ using the same techniques as in [GST] to…

This paper is mainly concerned with the existence of ground state sign-changing solutions for a class of second order quasilinear elliptic equations in bounded domains which derived from nonlinear optics models. Combining a non-Nehari…

In this paper, our goal is to investigate the existence of multiple nodal solutions to a class of planar Stein-Weiss problems involving a nonlinearity $f$ with subcritical or critical growth in the sense of Trudinger-Moser. To achieve this,…

We consider a class of stationary Schr\"{o}dinger-Poisson systems with a general nonlinearity $f(u)$ and coercive sign-changing potential $V$ so that the Schr\"{o}dinger operator $-\Delta+V$ is indefinite. Previous results in this framework…

We study the existence of nonradial sign-changing solutions to the Schroedinger-Poisson system in dimension N>=3. We construct nonradial sign-changing multi-peak solutions whose peaks are displaced in suitable symmetric configurations and…

We study a class of nonlinear schr\"{o}dinger system with external sources terms as perturbations in order to obtain existence of multiple solutions, this system arises from Bose-Einstein condensates etc..As these external sources terms are…

We study the Choquard equation involving mixed local and nonlocal operators $$-\Delta u+(-\Delta)^{s}u+V(x)u=(\frac{1}{|x|^{\mu}}* F(u))f(u)\quad\text{in }\R^{2},$$ where $s\in(0,1)$, $\mu\in(0,2)$, $F(t)=\int_{0}^{t} f(\tau)\,d\tau$, and…

We use a variant of the fountain Theorem to prove the existence of infinitely many weak solutions for the following fractional p-Laplace equation (-\Delta)^{s}_{p}u+V(x)|u|^{p-2}u=f(x,u) in R^N, where $s \in (0,1)$,$ p \geq 2$,$ N \geq 2$,…

We study the existence and multiplicity of sign changing solutions of the following equation $ \begin{cases} -\Delta u = \mu |u|^{2^{\star}-2}u+\frac{|u|^{2^{*}(t)-2}u}{|x|^t}+a(x)u \quad\text{in}\quad \Omega, u=0…

We prove that a class of superlinear indefinite problems with homogeneous Neumann boundary conditions admits an arbitrarily high number of positive solutions, provided that the parameters of the problem are adequately chosen. The…

In this paper, we use the method of invariant sets of descending flows to demonstrate the existence of multiple sign-changing solutions for a class of elliptic problems with zero Dirichlet boundary conditions. By combining Nehari manifold…