Existence of standing waves solution for a Nonlinear Schrödinger equations in ${\mathbb{R}}^N$

Abstract

In this paper, we investigate the existence of positive solution for the following class of elliptic equation $$ - ε^{2}Δu +V(x)u= f(u) \,\,\,\, \mbox{in} \,\,\, \mathbb{R}^{N}, $$ where $\epsilon >0$ is a positive parameter, $f$ has a subcritical growth and $V$ is a positive potential verifying some conditions.

References in corpus (2)

• A concentration phenomenon for semilinear elliptic equations
• Existence of positive solution for a nonlinear elliptic equation with saddle-like potential and nonlinearity with exponential critical growth in ${\mathbb{R}}^2$