Journal of Inequalities and Applications 
Volume 2007 (2007), Article ID 58363, 8 pages
doi:10.1155/2007/58363
Research Article

Superlinear Equations Involving Nonlinearities Limited by Asymptotically Homogeneous Functions

Sebastián Lorca,1 Marco Aurelio Souto,2 and Pedro Ubilla3

 1Instituto de Alta Investigación, Universidad de Tarapacá, Casilla 7–D, Arica 1000007, Chile
2Departamento de Matemática e Estatística, Universidade Federal de Campina Grande, Campina Grande 58109-900, PR, Brazil
3Departamento de Matemáticas y Ciencias de la Computación, Universidad de Santiago de Chile, Casilla 307, Correo 2, Santiago 9170022, Chile
Received 24 August 2006; Revised 24 November 2006; Accepted 28 March 2007

Recommended by Y. Giga

Abstract

We obtain a solution of the quasilinear equation −Δpu=f(u) in Ω, u=0, on ∂Ω. Here the nonlinearity f is superlinear at zero, and it is located near infinity between two functions that belong to a class of functions where the Ambrosetti-Rabinowitz condition is satisfied. More precisely, we consider the class of functions that are asymptotically homogeneous of index q.