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Existence of positive solutions for a semipositone p-Laplacian problem

Part of: Elliptic equations and systems

Published online by Cambridge University Press:  16 May 2016

Alfonso Castro ,
Djairo G. de Figueredo  and
Emer Lopera
Alfonso Castro
Affiliation:
Department of Mathematics, Harvey Mudd College, Claremont, CA 91711, USA (castro@g.hmc.edu)
Djairo G. de Figueredo
Affiliation:
Instituto de Matemática, Estatística e Computaҫão Cientifica, Universidade Estadual de Campinas, Caixa Postal 6065, Campinas, SP 13083-859, Brazil (djairo@ime.unicamp.br)
Emer Lopera
Affiliation:
Escuela de Matemáticas, Universidad Nacional de Colombia, Sede Medellín, Apartado Aéreo 3840, Medellín, Colombia (edlopera@unal.edu.co)
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We prove the existence of positive solutions to a semipositone p-Laplacian problem combining mountain pass arguments, comparison principles, regularity principles and a priori estimates.

Keywords

mountain pass theoremsemipositone problempositive solutionsp-Laplacianmaximum principlesa priori estimates

MSC classification

Secondary: 35J92: Quasilinear elliptic equations with $p$-Laplacian 35J20: Variational methods for second-order elliptic equations 35J60: Nonlinear elliptic equations
Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 146 , Issue 3 , June 2016 , pp. 475 - 482
Copyright
Copyright © Royal Society of Edinburgh 2016