Multiplicity theorems for nonlinear nonhomogeneous Robin problems

Abstract

We study a nonlinear Robin boundary value driven by a nonhomogeneous differential operator with a Carathéodory reaction and we look for multiple nontrivial solutions with sign information. We prove four such multiplicity theorems producing three nontrivial solutions, for resonant problems and for problems in which no global growth restriction is assumed on the reaction. Also, in the semilinear case, we show that we can have four nontrivial solutions, by producing a second nodal solution.