Open Access

Superlinear Equations Involving Nonlinearities Limited by Asymptotically Homogeneous Functions

Journal of Inequalities and Applications20072007:058363

https://doi.org/10.1155/2007/58363

Received: 24 August 2006

Accepted: 28 March 2007

Published: 17 May 2007

Abstract

We obtain a solution of the quasilinear equation in , , on . Here the nonlinearity 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 .

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Authors’ Affiliations

(1)
Instituto de Alta Investigación, Universidad de Tarapacá
(2)
Departamento de Matemática e Estatística, Universidade Federal de Campina Grande
(3)
Departamento de Matemáticas y Ciencias de la Computación, Universidad de Santiago de Chile

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Copyright

© Sebastiáan Lorca et al. 2007

This article is published under license to BioMed Central Ltd. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.