## Differential and Integral Equations

### Positive homoclinic solutions to some Schrödinger type equations

#### Abstract

By means of variational methods we prove the existence of a positive, homoclinic solution to an equation of the kind $u''=au-bu^p$, where $p>1$, and both coefficients $a(x)$, $b(x)$ are positive and asymptotically constant. Our main result requires a control from above on the ratios $M/\alpha$ and $\beta/\nu$, where $M=\sup a$, $\alpha=a(\infty)$, $\nu=\inf b$, $\beta=b(\infty)$.

#### Article information

Source
Differential Integral Equations Volume 29, Number 7/8 (2016), 665-682.

Dates
First available in Project Euclid: 3 May 2016