Multiplicity result for mixed local and nonlocal Kirchhoff problem involving critical growth

TL;DR

This paper proves the existence of multiple solutions for a mixed local and nonlocal Kirchhoff problem with critical growth, using advanced variational methods.

Contribution

It introduces a novel approach combining Nehari manifold and fibering map analysis to establish multiplicity results for complex Kirchhoff problems.

Findings

Existence of at least two nonnegative solutions.

Application of Nehari manifold method to mixed local and nonlocal problems.

Handling of critical nonlinearity with sign-changing weights.

Abstract

In this paper, we study the multiplicity of nonnegative solutions for mixed local and non-local problem involving critical nonlinearity with sign changing weight. Using Nehari manifold method and fibering map analysis, we have shown existence of two solutions.