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      Permanent link:
      https://www.ias.ac.in/article/fulltext/pmsc/113/03/0293-0319

    • Keywords

       

      Maximal monotone operator; pseudomonotone operator; Hartman condition; vectorp-Laplacian; convex and nonconvex problems; Leray-Schauder alternative

    • 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.

    • Author Affiliations

       

      Leszek Gasiński1 Nikolaos S Papageorgiou1 2

      1. Institute of Computer Science, Jagiellonian University, Nawojki 11, Cracow - 30072, Poland
      2. Department of Mathematics, National Technical University, Zografou Campus, Athens - 15780, Greece
    • Dates

       
  • Proceedings – Mathematical Sciences | News

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