Neumann problems associated to nonhomogeneous differential operators in Orlicz--Sobolev spaces

TL;DR

This paper investigates a nonlinear Neumann boundary value problem involving nonhomogeneous differential operators within Orlicz--Sobolev spaces, establishing conditions for the existence of nontrivial solutions considering nonlinearity and bifurcation effects.

Contribution

It introduces new existence criteria for solutions to Neumann problems with nonhomogeneous operators in Orlicz--Sobolev spaces, accounting for nonlinearities and bifurcation parameters.

Findings

Established sufficient conditions for solution existence.

Analyzed the interplay between nonlinearity and bifurcation.

Extended the theory to nonhomogeneous differential operators in Orlicz--Sobolev spaces.

Abstract

We study a nonlinear Neumann boundary value problem associated to a nonhomogeneous differential operator. Taking into account the competition between the nonlinearity and the bifurcation parameter, we establish sufficient conditions for the existence of nontrivial solutions in a related Orlicz--Sobolev space.