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The method of upper–lower solutions for nonlinear second order differential inclusions

✍ Scribed by Nikolaos S. Papageorgiou; Vasile Staicu

Publisher: Elsevier Science
Year: 2007
Tongue: English
Weight: 351 KB
Volume: 67
Category: Article
ISSN: 0362-546X
DOI: 10.1016/j.na.2006.06.023

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✦ Synopsis

In this paper we consider a second order differential inclusion driven by the ordinary p-Laplacian, with a subdifferential term, a discontinuous perturbation and nonlinear boundary value conditions. Assuming the existence of an ordered pair of appropriately defined upper and lower solutions ϕ and ψ respectively, using truncations and penalization techniques and results from nonlinear and multivalued analysis, we prove the existence of solutions in the order interval [ψ, ϕ] and of extremal solutions in [ψ, ϕ]. We show that our problem incorporates the Dirichlet, Neumann and Sturm-Liouville problems. Moreover, we show that our method of proof also applies to the periodic problem.

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