Electronic Journal of Differential Equations,
Vol. 2001(2001), No. 11, pp. 1-12.
Title: Existence of positive solutions to a superlinear elliptic problem
Authors: C. O. Alves (Univ.Federal da Paraiba, Brazil)
O. H. Miyagaki (Universidade Federal de Vicosa, Brazil)
Abstract:
We study the existence of positive solutions to
the semilinear elliptic problem
$$ - \epsilon^2 \Delta u + V(z) u = f(u) $$
in $\mathbb{R}^N$ ($N\geq 2$), where
the function $f$ has superlinear growth at infinity
without any restriction from aboveon its growth.
Submitted November 11, 2000. Published January 24, 2001.
Math Subject Classifications: 35J20, 35J10, 35A15.
Key Words: Superlinear; Mountain Pass; Schrodinger equation; elliptic equation.