Electronic Journal of Differential Equations,
Vol. 2010(2010), No. 61, pp. 1-23.
Title: Existence and concentration of positive solutions for a
quasilinear elliptic equation in R.
Author: Elisandra Gloss (Univ. Federal da Paraiba, Brazil)
Abstract:
We study the existence and concentration of positive
solutions for the quasilinear elliptic equation
$$
-\varepsilon^2u'' -\varepsilon^2(u^2)''u+V(x) u = h(u)
$$
in $\mathbb{R}$ as $\varepsilon\to 0$, where the potential
$V:\mathbb{R}\to \mathbb{R}$ has a positive infimum and
$\inf_{\partial \Omega}V>\inf_{ \Omega}V$ for some bounded
domain $\Omega$ in $\mathbb{R}$, and $h$ is a nonlinearity
without having growth conditions such as Ambrosetti-Rabinowitz.
Submitted January 16, 2010. Published May 05, 2010.
Math Subject Classifications: 35J20, 35J62.
Key Words: Schrodinger equation; quasilinear equation;
concentration; variational methods.