On double phase Kirchhoff problems with singular nonlinearity

TL;DR

This paper investigates the existence of multiple solutions for double phase Kirchhoff problems involving singular nonlinearities, using the fibering method and Nehari manifold, covering both degenerate and non-degenerate cases.

Contribution

It introduces a novel approach to establish multiplicity results for Kirchhoff problems with singular terms under broad assumptions.

Findings

Proved existence of at least two solutions with different energy signs.

Applied fibering method and Nehari manifold to handle singular and nonlinear terms.

Covered both degenerate and non-degenerate Kirchhoff cases.

Abstract

In this paper, we study multiplicity results for double phase problems of Kirchhoff type with right-hand sides that include a parametric singular term and a nonlinear term of subcritical growth. Under very general assumptions on the data, we prove the existence of at least two weak solutions that have different energy sign. Our treatment is based on the fibering method in form of the Nehari manifold. We point out that we cover both the non-degenerate as well as the degenerate Kirchhoff case in our setting.