Nodal solutions for nonlinear nonhomogeneous Robin problems

Abstract

We consider the nonlinear Robin problem driven by a nonhomogeneous differential operator plus an indefinite potential. The reaction term is a Carathéodory function satisfying certain conditions only near zero. Using suitable truncation, comparison, and cut-off techniques, we show that the problem has a sequence of nodal solutions converging to zero in the $C^1(\overline{\Omega })$-norm.

arXiv admin note: text overlap with arXiv:1811.04417