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Three Solutions for a Neumann Partial Differential Inclusion Via Nonsmooth Morse Theory

Abstract

We study a partial differential inclusion, driven by the p-Laplacian operator, involving a p-superlinear nonsmooth potential, and subject to Neumann boundary conditions. By means of nonsmooth critical point theory, we prove the existence of at least two constant sign solutions (one positive, the other negative). Then, by applying the nonsmooth Morse identity, we find a third non-zero solution.

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Correspondence to Antonio Iannizzotto.

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Colasuonno, F., Iannizzotto, A. & Mugnai, D. Three Solutions for a Neumann Partial Differential Inclusion Via Nonsmooth Morse Theory. Set-Valued Var. Anal 25, 405–425 (2017). https://doi.org/10.1007/s11228-016-0387-2

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Keywords

  • P-Laplacian
  • Partial differential inclusion
  • Morse theory

Mathematics Subject Classification (2010)

  • 49J52
  • 49K24
  • 58E05