### Existence of minimal nodal solutions for the nonlinear Schrödinger equations with $V(\infty)=0$

#### Abstract

We consider the problem $\Delta u+V(x)u=f'(u)$ in $\mathbb R^N$. Here the nonlinearity has a double power behavior and $V$ is invariant under an orthogonal involution, with $V(\infty)=0$. An existence theorem of one pair of solutions which changes sign exactly once is given.

#### Article information

Source
Adv. Differential Equations Volume 11, Number 12 (2006), 1375-1396.

Dates
First available in Project Euclid: 18 December 2012

Ghimenti, M.; Micheletti, A. M. Existence of minimal nodal solutions for the nonlinear Schrödinger equations with $V(\infty)=0$. Adv. Differential Equations 11 (2006), no. 12, 1375--1396. https://projecteuclid.org/euclid.ade/1355867589.