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Title: The method of upper-lower solutions for nonlinear second order differential inclusions
Author: Papageorgiou, Nikolaos
Staicu, Vasile
Keywords: Upper and lower solutions
Extremal solutions
Truncation and penalty functions
Fixed points
Issue Date: 2007
Publisher: Elsevier
Abstract: 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.
Peer review: yes
ISSN: 0362-546X
Appears in Collections:DMat - Artigos

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