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.