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Existence of solutions and periodic solutions for nonlinear evolution inclusions

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Abstract

In this paper we consider nonlinear-dependent systems with multivalued perturbations in the framework of an evolution triple of spaces. First we prove a surjectivity result for generalized pseudomonotone operators and then we establish two existence theorems: the first for a periodic problem and the second for a Cauchy problem. As applications we work out in detail a periodic nonlinear parabolic partial differential equation and an optimal control problem for a system driven by a nonlinear parabolic equation.

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Authors and Affiliations

  1. Department of Mathematics, National Technical University, Zografou Campus, 15773, Athens, Greece

    Nikolaos S. Papageorgiou

  2. Department of Mathematics, Via Vanvitelli, 1, Perugia, 06123, Italy

    Francesca Papalini & Francesca Renzacci

Authors
  1. Nikolaos S. Papageorgiou
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  2. Francesca Papalini
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  3. Francesca Renzacci
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Papageorgiou, N.S., Papalini, F. & Renzacci, F. Existence of solutions and periodic solutions for nonlinear evolution inclusions. Rend. Circ. Mat. Palermo 48, 341–364 (1999). https://doi.org/10.1007/BF02857308

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  • DOI: https://doi.org/10.1007/BF02857308

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