Michael E. Filippakis, Nikolaos S. Papageorgiou
We consider a nonlinear nonhomogeneous Robin problem that has the sum of a p-Laplacian and a q-Laplacian (a (p,q)-equation). The reaction term is a Caratheodory function which is resonant at with respect to any nonprincipal variational eigenvalue of the Robin p-Laplacian. Using variational methods and Morse theory (critical groups), we show the existence of at least three nontrivial smooth solutions.
Submitted October 4, 2017. Published January 2, 2018.
Math Subject Classifications: 35J20, 35J92, 58E05.
Key Words: (p,q)-Laplace differential operator; resonance; critical groups; multiple solutions; nonlinear regularity.
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| Michael E. Filippakis|
Department of Digital Systems
University of Piraeus
Piraeus 18536, Greece
| Nikolaos S. Papageorgiou |
Department of Mathematics
National Technical University of Athens
Zografou Campus, Athens 15780, Greece
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