article

Title: A positive solution for a nonlinear Schroedinger equation on $R^N$

Authors: Louis Jeanjean and Kazunaga Tanaka

Issue: Volume 54 (2005), Issue 2, 443-464

Abstract:

$We prove the existence of a positive solution for a class of equations of the form $-\Delta u + V(x)u = f(u)$, $u \in H^1(\mathbb{R}^N)$. On the nonlinearity $f$, only conditions around $0$ and at $\infty$ are required.$