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Nonlinear elliptic problems of Neumann-type

Rendiconti del Circolo Matematico di Palermo volume 50, pages 47–66 (2001)Cite this article

Abstract

In this paper we study a nonlinear elliptic differential equation driven by thep-Laplacian with a multivalued boundary condition of the Neumann type. Using techniques from the theory of maximal monotone operators and a theorem of the range of the sum of monotone operators, we prove the existence of a (strong) solution.

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Authors and Affiliations

  1. Department of Mathematics, Southwest Missouri State University, 65804, Springfiled, MO

    Shouchuan Hu

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

    N. S. Papageorgiou

Authors
  1. Shouchuan Hu
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  2. N. S. Papageorgiou
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Hu, S., Papageorgiou, N.S. Nonlinear elliptic problems of Neumann-type. Rend. Circ. Mat. Palermo 50, 47–66 (2001). https://doi.org/10.1007/BF02843918

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  • DOI: https://doi.org/10.1007/BF02843918

1991 Mathematica Subject Classification

  • 35J60
  • 35J25

Key words and phrases

  • Neumann problems
  • maximal monotone operators
  • subdifferentials
  • boundedly inversely compact
  • equality in the sense of distributions
  • trace maps and spaces