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

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.