Electron. J. Diff. Equ., Vol. 2013 (2013), No. 66, pp. 1-10.

Global branching for discontinuous problems involving the p-Laplacian

Guowei Dai, Ruyun Ma

Abstract:
In this article, we study elliptic problems with discontinuous nonlinearities involving the p-Laplacian both in bounded and unbounded domains. We prove that there exists a global branch of positive solutions under some suitable assumptions of the nonlinearities. Our results extend the corresponding ones of the Laplacian due to Ambrosetti, et al.

Submitted July 23, 2012. Published March 5, 2013.
Math Subject Classifications: 35B32, 34B18, 35R70.
Key Words: Global bifurcation; p-Laplacian

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Guowei Dai
Department of Mathematics, Northwest Normal University
Lanzhou, 730070, China
email: daiguowei@nwnu.edu.cn Tel: +86 931 7971297
Ruyun Ma
Department of Mathematics, Northwest Normal University
Lanzhou, 730070, China
email: mary@nwnu.edu.cn

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