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.

References in corpus (5)

• Regularity for minimizers for functionals of double phase with variable exponents
• Existence and multiplicity of solutions for double-phase Robin problems
• Positive solutions for singular double phase problems
• Existence of solutions for singular double phase problems via the Nehari manifold method
• Combined effects of singular and superlinear nonlinearities in singular double phase problems in ${\mathbb{R}}^N$