# Nodal solutions for nonlinear nonhomogeneous Robin problems

## TL;DR

This paper establishes the existence of a sequence of nodal solutions for a nonlinear Robin boundary value problem involving a nonhomogeneous differential operator and indefinite potential, with solutions converging to zero.

## Contribution

It introduces new methods to prove the existence of nodal solutions for complex nonlinear Robin problems with indefinite potentials.

## Key findings

- Existence of a sequence of nodal solutions converging to zero.
- Solutions are obtained using truncation, comparison, and cut-off techniques.
- Solutions converge in the $C^1(ar{
abla})$-norm.

## Abstract

We consider the nonlinear Robin problem driven by a nonhomogeneous differential operator plus an indefinite potential. The reaction term is a Carath\'eodory 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.