Strongly nonlinear multivalued boundary value problems

✍ Scribed by Leszek Gasiński; Nikolaos S. Papageorgiou

• Book ID: 104330418
• Publisher: Elsevier Science
• Year: 2003
• Tongue: English
• Weight: 187 KB
• Volume: 52
• Category: Article
• ISSN: 0362-546X
• DOI: 10.1016/s0362-546x(02)00162-1

✦ Synopsis

In this paper we study nonlinear second-order di erential inclusions involving the di erential operator depending on both: unknown function x and its derivative x , a multivalued maximal monotone operator and nonlinear multivalued boundary conditions. Our framework is general and can be applied to the classical boundary value problems, namely the Dirichlet, the Neumann and the periodic problems. Using notions and techniques from the nonlinear operator theory and from multivalued analysis, we obtain solutions for both the "convex" and "nonconvex" problems. Finally, we present the cases of special interest, which ÿt into our framework, illustrating the generality of our results.