Opuscula Math. 39, no. 2 (2019), 159-174
https://doi.org/10.7494/OpMath.2019.39.2.159
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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- Gabriele Bonanno
https://orcid.org/0000-0003-4115-7963
- University of Messina, Department of Engineering, C. da Di Dio (S. Agata), 98166 Messina, Italy
- Giuseppina D'Aguì
https://orcid.org/0000-0003-2080-8181
- University of Messina, Department of Engineering, C. da Di Dio (S. Agata), 98166 Messina, Italy
- 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.