Electron. J. Differential Equations, Vol. 2018 (2018), No. 127, pp. 1-21.

Asymmetric Robin boundary-value problems with p-Laplacian and indefinite potential

Salvatore A. Marano, Nikolaos S. Papageorgiou

Four nontrivial smooth solutions to a Robin boundary-value problem with p-Laplacian, indefinite potential, and asymmetric nonlinearity super-linear at infinity are obtained, all with sign information. The semilinear case is also investigated, producing a nonzero fifth solution. Our proofs use variational methods, truncation techniques, and Morse theory.

Submitted June 2, 2018. Published June 18, 2018.
Math Subject Classifications: 35J20, 35J60, 58E05.
Key Words: Robin boundary condition; p-Laplacian; indefinite potential; asymmetric reaction; superlinear at infinity; resonance; multiple solutions

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Salvatore A. Marano
Department of Mathematics and Computer Sciences
University of Catania
Viale A. Doria 6, 95125 Catania, Italy
email: marano@dmi.unict.it
  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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