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

Abstract

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.

Keywords

• Robin boundary condition
• p-Laplacian
• indefinite potential
• asymmetric reaction
• superlinear at infinity
• resonance
• multiple solutions