相关论文: Fully sign-changing Nehari constraint vs sign-chan…
We propose existence and multiplicity results for the system of Schr\"odinger equations with sign-changing nonlinearities in bounded domains or in the whole space $\mathbb{R}^N$. In the bounded domain we utilize the classical approach via…
We are looking for solutions to nonlinear Schr\"odinger-type equations of the form $$ (-\Delta)^{\alpha / 2} u (x) + V(x) u(x) = h (x,u(x)), \quad x \in \mathbb{R}^N, $$ where $V : \mathbb{R}^N \rightarrow \mathbb{R}$ is an external…
In this paper, we study the non-homogeneous nonlinear Schr\"{o}dinger system $$\left\{ \begin{array}{ll} -\triangle u_j+V_j(x) u_j=g_j(x,u_1,\cdots,u_m)+h_j(x),& x\in \Omega,\\ \\ u_j:=u_j(x)=0,& x\in \partial\Omega,\\ \\ j=1,2,\cdots,m,…
In this paper, we study the existence of localized sign-changing (or nodal) solutions for the following nonlinear Schr\"odinger-Poisson system \begin{equation*} \begin{cases} -\varepsilon^2 \Delta u+V(x)u+\phi…
In this paper, we consider the following nonlinear Schr\"odinger system: -$\Delta$ u+P(x)u=$\mu_1$ $u^3$+$\beta$ u$v^2$, x $\in$ $R^3$,\\ -$\Delta$ v+Q(x)v=$\mu_2$ $v^3$+$\beta$ $u^2$v, x $\in$ $R^3$, where $P(x),Q(x)$ are positive radial…
We prove the existence of infinitely many high energy sign-changing solutions for some classes of Schrodinger-Poisson systems in bounded domains, with nonlinearities having subcritical or critical growth. Our approach is variational and…
We study the following coupled Schr\"{o}dinger equations which have appeared as several models from mathematical physics: {displaymath} {cases}-\Delta u_1 +\la_1 u_1 = \mu_1 u_1^3+\beta u_1 u_2^2, \quad x\in \Omega, -\Delta u_2 +\la_2 u_2…
We are concerned with the multiplicity of positive solutions for the singular superlinear and subcritical Schr\"odinger equation $$ \begin{array}{c} -\Delta u +V(x)u=\lambda a(x)u^{-\gamma}+b(x)u^{p}~\mbox{in}~ \mathbb{R}^{N}, \end{array}…
We investigate the existence of multiple bound state solutions, in particular sign-changing solutions. By using the method of invariant sets of descending flow, we prove that this system has infinitely many sign-changing solutions. In…
We show that the components of finite energy solutions to general nonlinear Schr\"odinger systems have exponential decay at infinity. Our results apply to positive or sign-changing components, and to cooperative, competitive, or…
In this paper, we study the existence of multiple positive solutions for a class of fractional Schr\"{o}dinger-Poisson systems involving sign-changing potential and critical nonlinearities on an unbounded domain. With the help of Nehari…
In this work, we establish the existence of solutions that change sign at low energy for a non-local weighted Kirchhoff problem in the set $\mathbb{R}^{N}, N>2$. The non-linearity of the equation is assumed to have exponential growth in…
In this paper we consider the following Schr\"odinger-Poisson system in the whole $\mathbb R^{3}$, \begin{equation*} \left\{ \begin{array}{ll} -\Delta u+u+ \lambda \phi u=f(u) &\text{ in } \mathbb R^3, -\Delta \phi= u^2 &\text{ in } \mathbb…
We study the existence of positive and sign-changing multipeak solutions for the stationary Nonlinear Schroedinger Equation. Here no symmetry on $V$ is assumed. It is known that this equation has positive multipeak solutions with all peaks…
We investigate an energy-subcritical defocusing nonlinear Schr\"odinger equation in $\mathbb R^3$ subject to a lower order nonlinear trapping potential and a spatially dependent nonlinear damping: \begin{equation*} i\partial_t u + \Delta u…
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…
We find positive non-radial solutions for a system of Schr\"odinger equations in a weak fully attractive or repulsive regime in presence of an external radial trapping potential that exhibits a maximum or a minimum at infinity.
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…
Coupled nonlinear Schrodinger systems describe some physical phenomena such as the propagation in birefringent optical fibers, Kerr-like photorefractive media in optics and Bose-Einstein condensates. In this paper, we study the existence of…
We revisit the following nonlinear Schr\"odinger system \begin{align*}\begin{cases} -\epsilon^{2}\Delta u +P(x) u= \mu_1 u^3 +\beta uv^2, &~\text{in}\;\mathbb {R}^3,\\ -\epsilon^{2}\Delta v+Q(x) v= \mu_2 v^3 +\beta u^2v,…