Related papers: Ground state of indefinite coupled nonlinear Schr\…

In this paper, by adapting the perturbation method, we study normalized standing wave solutions for the following nonlinear Schr\"odinger-Bopp-Podolsky system: - Delta u + q(x) phi u = omega u + f(u) in Omega, - Delta phi + a^2 Delta^2 phi…

We establish the uniqueness of ground states of some coupled nonlinear Schrodinger systems in the whole space. We firstly use Schwartz symmetrization to obtain the existence of ground states for a more general case. To prove the uniqueness…

We prove the existence of radial and radially decreasing ground states of an m-coupled nonlinear Schrodinger equation with a general nonlinearity.

We prove the existence of a nontrivial groundstate solution for the class of nonlinear Choquard equation $$ -\Delta u+u=(I_\alpha*F(u))F'(u)\qquad\text{in }\mathbb{R}^2, $$ where $I_\alpha$ is the Riesz potential of order $\alpha$ on the…

In this article, we study the existence of normalized ground state solutions for the following biharmonic nonlinear Schr\"{o}dinger equation with combined nonlinearities \begin{equation*} \Delta^2u=\lambda u+\mu|u|^{q-2}u+|u|^{p-2}u,\quad…

We consider the following coupled fractional Schr\"{o}dinger system: \begin{equation*} \left\{ \begin{aligned} &(-\Delta)^su+\lambda_1u=\mu_1|u|^{2p-2}u+\beta|v|^p|u|^{p-2}u\\ &(-\Delta)^sv+\lambda_2v=\mu_2|v|^{2p-2}v+\beta|u|^p|v|^{p-2}v\\…

In the present work we are concerned with the existence of normalized solutions to the following Schr\"odinger-Poisson System $$ \left\{ \begin{array}{ll} -\Delta u + \lambda u + \mu (\ln|\cdot|\ast |u|^{2})u = f(u) \textrm{ \ in \ }…

In this paper we are interested in the following nonlinear Choquard equation $$ -\Delta u+(\lambda V(x)-\beta)u =\big(|x|^{-\mu}\ast |u|^{2_{\mu}^{\ast}}\big)|u|^{2_{\mu}^{\ast}-2}u\hspace{4.14mm}\mbox{in}\hspace{1.14mm} \mathbb{R}^N, $$…

We construct solutions to the nonlinear magnetic Schr\"odinger equation $$ \left\{ \begin{aligned} - \varepsilon^2 \Delta_{A/\varepsilon^2} u + V u &= \lvert u\rvert^{p-2} u & &\text{in}\ \Omega,\\ u &= 0 & &\text{on}\ \partial\Omega,…

This work is devoted to the Dirichlet problem for the equation (-\Delta u = \lambda u + |x|^\alpha |u|^{2^*-2} u) in the unit ball of $\mathbb{R}^N$. We assume that $\lambda$ is bigger than the first eigenvalues of the laplacian, and we…

We are interested in the existence and asymptotic behavior of ground states of the following normalized nonlocal semilinear problem: \[ \begin{cases} - \Delta u + (V - \omega) u + (K_{a, b} \ast u^2) u = 0 &\text{in} ~ \mathbb{R}^3; \\…

In this paper we consider a two component system of coupled non linear Schr\"odinger equations modeling the phase separation in the binary mixture of Bose-Einstein condensates and other related problems. Assuming the existence of solutions…

We study the energy-critical focusing nonlinear Schr\"odinger equation with an energy- subcritical perturbation. We show the existence of a ground state in the four or higher dimensions. Moreover, we give a sufficient and necessary…

We study the following nonlinear Schr\"odinger-Bopp-Podolsky system \[ \begin{cases} -\Delta u + \omega u + q^{2}\phi u = |u|^{p-2}u -\Delta \phi + a^2 \Delta^2 \phi = 4\pi u^2 \end{cases} \hbox{ in }\mathbb{R}^3 \] with $a,\omega>0$. We…

The aim of this work is the study of the existence of normalized solutions to the nonlinear Schr\"odinger equation with nonlocal nonlinearities: \begin{equation}\nonumber \left\{\begin{aligned} &-\Delta u =\lambda…

In this paper, we are concerned with the ground state solutions of nonlinear fractional Schr\"odinger equation involving critical growth. Without Ambrosetti-Rabinowitz condition and monotonicity condition on the nonlinearity, we get the…

We focus on the study of ground-states for the system of $M$ coupled semilinear Schr\"odinger equations with power-type nonlinearities and couplings. We extend the characterization result from a previous work (arXiv:1410.7993) to the case…

In this paper we deal with the cubic Schr\"odinger system $ -\Delta u_i = \sum_{j=1}^n \beta_{ij}u_j^2 u_i$, $u_1,\dots,u_n \geq 0$ in $\mathbb{R}^N (N\leq 3)$, where $\beta=(\beta_{i,j})_{ij}$ is a symmetric matrix with real coefficients…

In this paper, we study the following nonlinear Schr\"odinger-Poisson type equation \begin{equation*} \begin{cases} -\varepsilon^2\Delta u+V(x)u+K(x)\phi u=f(u)&\text{in}\ \mathbb{R}^3,\\ -\varepsilon^2\Delta \phi=K(x)u^2&\text{in}\…

We study the existence of positive bound states for the nonlinear elliptic system \[ \begin{cases} - \Delta u_i + \lambda_i u_i = \sum_{j=1}^d \beta_{ij} u_j^2 u_i & \text{in $\Omega$} \\ u_1 =\cdots = u_d=0 & \text{on $\partial \Omega$},…