Electron. J. Differential Equations, Vol. 2018 (2018), No. 01, pp. 1-24.

Resonant (p,q)-equations with Robin boundary condition

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 $\pm\infty$ 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
email: mfilip@unipi.gr
Nikolaos S. Papageorgiou
Department of Mathematics
National Technical University of Athens
Zografou Campus, Athens 15780, Greece
email: npapg@math.ntua.gr

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