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

In this paper the question of finding infinitely many solutions to the problem $-\Delta u+a(x)u=|u|^{p-2}u$, in $\mathbb{R}^N$, $u \in H^1(\mathbb{R}^N)$, is considered when $N\geq 2$, $p \in (2, 2N/(N-2))$, and the potential $a(x)$ is a…

This paper is devoted to study the existence and multiplicity solutions for the nonlinear Schr\"odinger-Poisson systems involving fractional Laplacian operator: \begin{equation}\label{eq*} \left\{ \aligned &(-\Delta)^{s} u+V(x)u+ \phi…

In this article, we prove the existence and multiplicity of positive solutions for the following fractional elliptic equation with sign-changing weight functions: \begin{eqnarray*} \left\{\begin{array}{l@{\quad }l} (-\Delta)^\alpha u=…

In this work we study the following class of systems of coupled nonlinear fractional nonlinear Schr\"odinger equations, \begin{equation*} \left \{ \begin{array}{l} (-\Delta)^s u_1+ \lambda_1 u_1= \mu_1 |u_1|^{2p-2}u_1+\beta |u_2|^{p}…

In this paper we prove an existence result of multiple positive solutions for the following quasilinear problem \begin{equation*} \left\{ \begin{array}[c]{ll} -\Delta u - \Delta (u^2)u = |u|^{p-2}u & \mbox{ in } \Omega u= 0 &\mbox{ on }…

We consider the following slightly supercritical problem for the Lane-Emden system with Neumann boundary conditions: \begin{equation*} \begin{cases} -\Delta u_1=|u_2|^{p_\epsilon-1}u_2,\ &in\ \Omega,\\ -\Delta u_2=|u_1|^{q_\epsilon-1}u_1, \…

The present study is concerned with the following Schr\"{o}dinger-Poisson system involving critical nonlocal term $$ \left\{ \begin{array}{ll} -\Delta u+u-K(x)\phi |u|^3u=\lambda f(x)|u|^{q-2}u, & x\in\mathbb{R}^3, -\Delta \phi=K(x)|u|^5, &…

We investigate the structure of nodal solutions for coupled nonlinear Schr\"{o}dinger equations in the repulsive coupling regime. Among other results, for the following coupled system of $N$ equations, we prove the existence of infinitely…

In this paper, we are concerned with the quasilinear Schr\"{o}dinger equation \begin{equation*} -\Delta u+V(x)u-u\Delta(u^2)=g(u),\ \ x\in \mathbb{R}^{N}, \end{equation*} where $N\geq3$, $V$ is radially symmetric and nonnegative, and $g$ is…

This paper concerns the existence of multiple solutions for the fractional logarithmic Schr\"odinger-Possion system of the form \begin{equation*} \begin{cases} {\varepsilon}^{2\alpha} (-\Delta )^{\alpha}u+V(x) u+\phi u=u \log u^{2}+u^{q-1},…

In this paper we consider the following quasilinear Schr\"odinger-Poisson system in a bounded domain in $\mathbb{R}^{2}$: $$ \left\{ \begin{array}[c]{ll} - \Delta u +\phi u = f(u) &\ \mbox{in } \Omega, -\Delta \phi - \varepsilon^{4}\Delta_4…

In this paper we prove the existence of infinitely many nontrivial solutions of the following equations driven by a nonlocal integro-differential operator $L_K$ with concave-convex nonlinearities and homogeneous Dirichlet boundary…

In this paper, we consider the following nonlinear Schr\"odinger system in $R^3$: \begin{align*} -\Delta u_j +P_j(x) u=\mu_j u_j^3+\sum\limits_{i=1,i\neq j}^N\beta_{ij}u_i^2u_j, \end{align*} where $N\geq3$, $P_j$ are nonnegative radial…

We study the nonlinear one-dimensional $p$-Laplacian equation $$ -(y'^{(p-1)})'+(p-1)q(x)y^{(p-1)}=(p-1)w(x)f(y) on (0,1),$$ with linear separated boundary conditions. We give sufficient conditions for the existence of solutions with…

In this paper we consider a class of fractional Schr\"odinger equations with potentials vanishing at infinity. By using a minimization argument and a quantitative deformation Lemma, we prove the existence of a sign-changing solution.

In this paper, we are concerned with the existence of the least energy sign-changing solutions for the following fractional Schr\"{o}dinger-Poisson system: \begin{align*} \left\{ \begin{aligned} &(-\Delta)^{s} u+V(x)u+\lambda\phi(x)u=f(x,…

We give an upper bound for the least energy of a sign-changing solution to the the nonlinear scalar field equation $$-\Delta u = f(u), \qquad u\in D^{1,2}(\mathbb{R}^{N}),$$ where $N\geq5$ and the nonlinearity $f$ is subcritical at infinity…

We prove the existence of one positive, one negative, and one sign-changing solution of a $p$-Laplacian equation on $\mathbb{R}^N$, with a $p$-superlinear subcritical term. Sign-changing solutions of quasilinear elliptic equations set on…

Very differently from those perturbative techniques of Deng-Musso in [26], we use the assumption of a $C^1$-stable critical point to construct positive or sign-changing solutions with arbitrary $m$ isolated bubbles to the boundary value…

In this paper, we consider existence of positive solutions for the Schr\"odinger quasilinear elliptic problem $$ \left\{ \begin{array}{l} \Delta_pu+\Delta_p(|u|^{2\gamma})|u|^{2\gamma-2}u = a(x)g(u)~ \mbox{on}~ \mathbb{R}^N,\\ u>0\…