Parametric superlinear double phase problems with singular term and critical growth on the boundary

TL;DR

This paper investigates quasilinear elliptic equations involving double phase operators with singular and superlinear reactions, establishing the existence of multiple solutions under certain conditions using advanced functional analysis techniques.

Contribution

It introduces a new norm for Musielak-Orlicz Sobolev spaces and applies the Nehari manifold and fibering method to prove multiple solutions for complex boundary value problems.

Findings

Existence of at least two weak solutions for small parameters

Development of a new norm for Musielak-Orlicz Sobolev spaces

Application of Nehari manifold and fibering method to boundary problems

Abstract

In this paper we study quasilinear elliptic equations driven by the double phase operator along with a reaction that has a singular and a parametric superlinear term and with a nonlinear Neumann boundary condition of critical growth. Based on a new equivalent norm for Musielak-Orlicz Sobolev spaces and the Nehari manifold along with the fibering method we prove the existence of at least two weak solutions provided the parameter is sufficiently small.