Electron. J. Diff. Eqns., Vol. 2001(2001), No. 11, pp. 1-12.

Existence of positive solutions to a superlinear elliptic problem

C. O. Alves & O. H. Miyagaki

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 above on 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.

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C. O. Alves
Universidade Federal da Paraiba
Departamento de Matematica
58109-970 - Campina Grande (PB), Brazil
e-mail: coalves@dme.ufpb.br
Olimpio H. Miyagaki
Universidade Federal de Vi\c cosa
Departamento de Matematica
36571-000 Vicosa-MG -Brazil
e-mail: olimpio@mail.ufv.br

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