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Nonlinear second-order multivalued boundary value problems

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Abstract

In this paper we study nonlinear second-order differential inclusions involving the ordinary vectorp-Laplacian, a multivalued maximal monotone operator and nonlinear multivalued boundary conditions. Our framework is general and unifying and incorporates gradient systems, evolutionary variational inequalities and 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 fit into our framework, illustrating the generality of our results.

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Authors and Affiliations

  1. Institute of Computer Science, Jagiellonian University, Nawojki 11, 30072, Cracow, Poland

    Leszek Gasiński & Nikolaos S. Papageorgiou

  2. Department of Mathematics, National Technical University, Zografou Campus, 15780, Athens, Greece

    Nikolaos S. Papageorgiou

Authors
  1. Leszek Gasiński
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  2. Nikolaos S. Papageorgiou
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Correspondence to Leszek Gasiński.

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Gasiński, L., Papageorgiou, N.S. Nonlinear second-order multivalued boundary value problems. Proc. Indian Acad. Sci. (Math. Sci.) 113, 293–319 (2003). https://doi.org/10.1007/BF02829608

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  • DOI: https://doi.org/10.1007/BF02829608

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