## 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

Permanent link to this document
https://projecteuclid.org/euclid.die/1462298680

Mathematical Reviews number (MathSciNet)
MR3498872

Zentralblatt MATH identifier
1363.34120

#### Citation

Gavioli, Andrea; Sanchez, Luís. Positive homoclinic solutions to some Schrödinger type equations. Differential Integral Equations 29 (2016), no. 7/8, 665--682. https://projecteuclid.org/euclid.die/1462298680