Positive solutions of the p-Laplacian involving a superlinear nonlinearity with zeros

Leonelo Iturriaga, Eugenio Massa, Justino Sánchez, Pedro Ubilla

Research output: Contribution to journalArticle

23 Citations (Scopus)

Abstract

Using a combination of several methods, such as variational methods, the sub and supersolutions method, comparison principles and a priori estimates, we study existence, multiplicity, and the behavior with respect to λ of positive solutions of p-Laplace equations of the form - Δpu = λ h (x, u), where the nonlinear term has p-superlinear growth at infinity, is nonnegative, and satisfies h (x, a (x)) = 0 for a suitable positive function a. In order to manage the asymptotic behavior of the solutions we extend a result due to Redheffer and we establish a new Liouville-type theorem for the p-Laplacian operator, where the nonlinearity involved is superlinear, nonnegative, and has positive zeros. © 2009 Elsevier Inc. All rights reserved.
Original languageEnglish
Pages (from-to)309-327
Number of pages19
JournalJournal of Differential Equations
DOIs
Publication statusPublished - 15 Jan 2010
Externally publishedYes

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