Related papers: Ground States for a nonlinear Schr\"odinger system…
In this paper, we consider the following nonlinear Schr\"{o}dinger equations with mixed nonlinearities: \begin{eqnarray*} \left\{\aligned &-\Delta u=\lambda u+\mu |u|^{q-2}u+|u|^{2^*-2}u\quad\text{in }\mathbb{R}^N,\\ &u\in…
We establish the existence of infinitely many nonnegative, segregated solutions for the sublinearly coupled Schr\"odinger system \begin{equation*} \left\{\begin{aligned}-\Delta u+K_1(x)u&=\mu u^{p-1}+ (\sigma_1+1)\beta…
We investigate the existence of ground states for the nonlinear Schr\"odinger Equation on star graphs with two subcritical focusing nonlinear terms: a standard power nonlinearity, and a delta-type nonlinearity located at the vertex. We find…
We determine and study the ground states of a focusing Schr\"odinger equation in dimension one with a power nonlinearity $|\psi|^{2\mu} \psi$ and a strong inhomogeneity represented by a singular point perturbation, the so-called…
We investigate the existence of ground states for the focusing Nonlinear Schr\"odinger Equation on the infinite three-dimensional cubic grid. We extend the result found for the analogous two-dimensional grid by proving an appropriate…
In this paper, we consider the following 2-D Schr\"{o}dinger-Newton equations \begin{eqnarray*} -\Delta u+a(x)u+\frac{\gamma}{2\pi}\left(\log(|\cdot|)*|u|^p\right){|u|}^{p-2}u=b{|u|}^{q-2}u \qquad \text{in} \,\,\, \mathbb{R}^{2},…
In this paper we study ground states of the following fractional Schr\"odinger equation (- \Delta)^{s} u + V(x) u = f(x, u) \, \mbox{ in } \, \R^{N}, u\in \H^{s}(\R^{N}) where $s\in (0,1)$, $N>2s$ and $f$ is a continuous function satisfying…
We prove the existence of ground state solutions for the nonlinear Schrodinger-Maxwell equations.
We investigate the existence and stability of ground states for the defocusing nonlinear Schr\"odinger equation on non-compact metric graphs. We establish a sharp criterion for the existence of action ground states in terms of the spectral…
In this paper, we deal with a class of planar Schr\"{o}dinger-Poisson systems, namely, $-\Delta u+V(x)u+\frac{\gamma}{2\pi}\bigl(\log(|\cdot|)\ast|u|^{2}\bigr)u=b|u|^{p-2}u\ \text{in}\ \mathbb{R}^{2}$, where $\gamma > 0$, $b \geq 0$, $p>2$…
We study uniqueness and nondegeneracy of ground states for stationary nonlinear Schr\"odinger equations with a focusing power-type nonlinearity and an attractive inverse-power potential. We refine the results of Shioji and Watanabe (2016)…
We consider the existence of multiple positive solutions to the nonlinear Schr\"odinger systems sets on $H^1(\mathbb{R}^N) \times H^1(\mathbb{R}^N)$, \[ \left\{ \begin{aligned} -\Delta u_1 &= \lambda_1 u_1 + \mu_1 |u_1|^{p_1 -2}u_1 + \beta…
In this paper we are concerned with the fractional Schr\"{o}dinger equation $(-\Delta)^{\alpha} u+V(x)u =f(x, u)$, $x\in \rn$, where $f$ is superlinear, subcritical growth and $u\mapsto\frac{f(x, u)}{\vert u\vert}$ is nondecreasing. When…
In this paper, we study the existence, non-existence and asymptotic behavior of positive ground states for the nonlinear Choquard equation: \begin{equation}\label{0.1} -\Delta u+\varepsilon u=\big(I_{\alpha}\ast F(u)\big)F'(u),\quad u\in…
We are concerned with the study of existence of nontrivial ground states solutions for of Schr\"odinger systems with Chern-Simons gauge fields.
In this paper, we study the following fractional Schr\"odinger equation: \[ \left\{\begin{gathered} {(- \Delta)^s}u + mu = f(u){\text{in}}{\mathbb{R}^N}, \hfill u \in {H^s}({\mathbb{R}^N}),{\text{}}u > 0{\text{on}}{\mathbb{R}^N}, \hfill \\…
We are concerned with the following nonlinear Schr\"odinger equation \begin{eqnarray*} \begin{aligned} \begin{cases} -\Delta u+\lambda u=f(u) \ \ {\rm in}\ \mathbb{R}^{2},\\ u\in H^{1}(\mathbb{R}^{2}),~~~ \int_{\mathbb{R}^2}u^2dx=\rho,…
In the present paper, we prove the existence of solutions $(\lambda, u)\in \R\times H^1(\R^N)$ to the following elliptic equations with potential $\displaystyle -\Delta u+(V(x)+\lambda)u=g(u)\;\hbox{in}\;\R^N, $ satisfying the normalization…
We consider a class of nonlinear Schr\"odinger equation in two space dimensions with an attractive potential. The nonlinearity is local but rather general encompassing for the first time both subcritical and supercritical (in $L^2$)…
In this article, we study the Schr\"{o}dinger-Newton equation \begin{equation} -\Delta u+\lambda u=\frac{1}{4\pi}\left(\frac{1}{|x|}\star u^{2}\right)u+|u|^{q-2}u \quad \text{in}~\mathbb{R}^3, \end{equation} where $\lambda\in\mathbb{R}_+$,…