Infinitely many smooth nodal solutions for Orlicz Robin problems

Abstract

In this note, we study a Robin problem driven by the Orlicz g-Laplace operator. In particular, by using a regularity result and Kajikiya’s theorem, we prove that the problem has a whole sequence of distinct smooth nodal solutions converging to the trivial one. The analysis is developed in the most general abstract setting that corresponds to Orlicz–Sobolev function spaces.