Opuscula Math. 39, no. 2 (2019), 159-174

Opuscula Mathematica

Nonlinear elliptic equations involving the p-Laplacian with mixed Dirichlet-Neumann boundary conditions

Gabriele Bonanno
Giuseppina D'Aguì
Angela Sciammetta

Abstract. In this paper, a nonlinear differential problem involving the \(p\)-Laplacian operator with mixed boundary conditions is investigated. In particular, the existence of three non-zero solutions is established by requiring suitable behavior on the nonlinearity. Concrete examples illustrate the abstract results.

Keywords: mixed problem, critical points.

Mathematics Subject Classification: 35J25, 35J20.

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  • Angela Sciammetta
  • University of Palermo, Department of Mathematics and Computer Science, Via Archirafi 34, 90123 Palermo, Italy
  • Communicated by Dušan Repovš.
  • Received: 2018-10-23.
  • Accepted: 2018-10-30.
  • Published online: 2018-12-07.
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Cite this article as:
Gabriele Bonanno, Giuseppina D'Aguì, Angela Sciammetta, Nonlinear elliptic equations involving the p-Laplacian with mixed Dirichlet-Neumann boundary conditions, Opuscula Math. 39, no. 2 (2019), 159-174, https://doi.org/10.7494/OpMath.2019.39.2.159

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