相关论文: Normalized Solutions on large smooth domains to th…

In this paper, we consider the existence and multiplicity of prescribed mass solutions to the following nonlinear Schrodinger equations with mixed nonlinearities. The standard approach based on the Pohozaev identity to obtain normalized…

The paper addresses an open problem raised in [Bartsch, Molle, Rizzi, Verzini: Normalized solutions of mass supercritical Schr\"odinger equations with potential, Comm. Part. Diff. Equ. 46 (2021), 1729-1756] on the existence of normalized…

This paper is concerned with the existence of normalized solutions of the nonlinear Schr\"odinger equation \[ -\Delta u+V(x)u+\lambda u = |u|^{p-2}u \qquad\text{in $\mathbb{R}^N$} \] in the mass supercritical and Sobolev subcritical case…

In this paper, we study the following Schr\"odinger equations with potentials and general nonlinearities \begin{equation*} \left\{\begin{aligned} & -\Delta u+V(x)u+\lambda u=|u|^{q-2}u+\beta f(u), \\ & \int |u|^2dx=\Theta, \end{aligned}…

We obtain the existence, nonexistence and multiplicity of positive solutions with prescribed mass for nonlinear Schr\"{o}dinger equations in bounded domains via a global bifurcation approach. The nonlinearities in this paper can be mass…

In this paper, we consider the existence of positive solutions with prescribed $L^2$-norm for the following nonlinear Schr\"{o}dinger equation involving potential and Sobolev critical exponent \begin{equation*} \begin{cases} -\Delta…

In present paper, we study the following nonlinear Schr\"{o}dinger equation with combined power nonlinearities \begin{align*} - \Delta u+V(x)u+\lambda u=|u|^{2^*-2}u+\mu |u|^{q-2}u \quad \quad \text{in} \ \mathbb{ R}^N, \ N\geq 3…

In this paper, we consider the existence, multiplicity and the asymptotic behavior of prescribed mass solutions to the following nonlinear Kirchhoff equation with mixed nonlinearities: -(a+b\int|\nabla u|^2\mathrm{d}x)\Delta u+V(x)u+\lambda…

In present paper, we prove the existence of solutions $(\lambda, u)\in \R\times H^1(\R^N)$ to the following Schr\"odinger equation $$ \begin{cases} -\Delta u(x)+V(x)u(x)+\lambda u(x)=g(u(x))\quad &\hbox{in}~\R^N\\ 0\leq u(x)\in H^1(\R^N),…

We study the existence, non-existence and multiplicity of prescribed mass positive solutions to a Schr\"odinger equation of the form \begin{equation*} -\Delta u+\lambda u=g(u), \quad u \in H^1(\mathbb{R}^N), \, N \geq 1. \end{equation*} Our…

We are concerned with solutions of the following quasilinear Schr\"odinger equations \begin{eqnarray*} -{\mathrm{div}}\left(\varphi^{2}(u) \nabla u\right)+\varphi(u) \varphi^{\prime}(u)|\nabla u|^{2}+\lambda u=f(u), \quad x \in…

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 consider the existence, multiplicity and nonexistence of solutions for the following equation \begin{equation*} \begin{cases} \begin{aligned} &-\Delta u+\omega u=\mu u^{p-1}+u^{q-1},~ u>0 \quad &&\text { in } \Omega, \\…

In this paper we study the existence of normalized solutions to the following nonlinear Schr\"{o}dinger equation with critical growth \begin{align*} \left\{ \begin{aligned} &-\Delta u=\lambda u+f(u), \quad \quad \hbox{in }\mathbb{R}^N,\\…

This paper investigates the existence of positive normalized solutions to the Sobolev critical Schr\"{o}dinger equation: \begin{equation*} \left\{ \begin{aligned} &-\Delta u +\lambda u =|u|^{2^*-2}u \quad &\mbox{in}& \ \Omega,\\…

This paper focuses on the existence of multiple normalized solutions to Schr\"{o}dinger equations with general nonlinearities in bounded domains via variational methods. We first obtain two positive normalized solutions, one is a normalized…

In this paper we prove the existence of normalized solutions $(\lambda,u)\subset (0,\infty)\times H^1(\mathbb{R}^3)$ to the following Schr\"{o}dinger-Poisson equation $$ \begin{cases} -\Delta u+V(x)u+\lambda u+(|x|^{-1}\ast…

We study the existence and nonexistence of normalized solutions $(u_a, \lambda_a)\in H^{1}(\mathbb{R}^N)\times \mathbb{R}$ to the nonlinear Schr\"{o}dinger equation with mixed nonlocal nonlinearities. This study can be viewed as a…

We consider the nonlinear Choquard equation $$\begin{cases} & - \Delta u = (I_\alpha \ast F(u))F'(u) -\mu u \ \text{in}\ \mathbb{R}^N, & u \in \ H^1(\mathbb{R}^N), \ \int_{\mathbb{R}^N} |u|^2 dx=m, \end{cases} $$ where $\alpha\in(0,N)$,…

In this paper, we deal with the existence and concentration of normalized solutions to the supercritical nonlinear Schr\"{o}dinger equation \begin{equation*} \left\{ \begin{array}{l} -\Delta u + V(x) u = \mu_q u + a|u|^q u \quad {\rm…