Nodal solutions for noncoercive nonlinear Neumann problems with indefinite potential

Abstract

We consider a nonlinear Neumann problem driven by a nonhomogeneous differential operator and an indefinite potential. Using variational methods together with flow invariance arguments, we show that the problem has at least one nodal solution. The result presented in this paper gives an answer to the open question raised by Papageorgiou and Rădulescu (2016).