On an anisotropic double phase problem with singular and sign changing nonlinearity

TL;DR

This paper investigates anisotropic double phase problems with singular and sign-changing nonlinearities, establishing multiple solutions in subcritical and critical cases using Nehari manifold techniques, including new results for the classical p-Laplacian.

Contribution

It introduces new existence results for solutions to anisotropic double phase problems with singular and sign-changing nonlinearities, including novel findings in the classical p-Laplacian case.

Findings

Existence of at least two opposite sign solutions in the subcritical case.

Existence of one negative energy solution in the critical case.

New results for the classical p-Laplacian in the critical case.

Abstract

This article consists of study of anisotropic double phase problems with singular term and sign changing subcritical as well as critical nonlinearity. Seeking the help of well known Nehari manifold technique, we establish existence of at least two opposite sign energy solutions in the subcritical case and one negative energy solution in the critical case. The results in the critical case is even new in the classical $p$-Laplacian case.