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Quasilinear Problems Involving Changing-Sign Nonlinearities without an Ambrosetti–Rabinowitz-Type Condition

Published online by Cambridge University Press:  16 April 2014

Leonelo Iturriaga ,
Marco A. Souto  and
Pedro Ubilla
Leonelo Iturriaga
Affiliation:
Departamento de Matemática, Universidad Técnica Federico Santa María, Avenida España 1680, Casilla 110-V, Valparaíso, Chile, (leonelo.iturriaga@gmail.com)
Marco A. Souto
Affiliation:
Departamento de Matemática e Estatística, Universidade Federal de Campina Grande, 58429-010 Campina Grande – PB, Brazil, (xlink:href="marco@dme.ufcg.edu.br">marco@dme.ufcg.edu.br)
Pedro Ubilla
Affiliation:
Departamento de Matemáticas y Computación, Universidad de Santiago de Chile, Casilla 307, Correo 2, Santiago, Chile, (pedro.ubilla@usach.cl)
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Abstract

In this paper quasilinear elliptic boundary value equations without an Ambrosetti and Rabinowitz growth condition are considered. Existence of a non-trivial solution result is established. For this, we show the existence of a Cerami sequence by using a variant of the mountain-pass theorem due to Schechter. The novelty here is that we may consider nonlinearities that satisfy a local p-superlinear condition and may change sign.

Keywords

variational methodscritical pointssuperlinear problems and quasilinear elliptic equationsPrimary 35J6035J2535J70
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 57 , Issue 3 , October 2014 , pp. 755 - 762
Copyright
Copyright © Edinburgh Mathematical Society 2014 

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