A Kirchhoff Problem Involving $$\overrightarrow{p}-$$Laplacian Operator

Abstract

In this paper, we investigate the existence of positive solutions for a Kirchhoff-type elliptic problem in anisotropic Sobolev spaces. The novelty of our approach lies in the use of anisotropic Sobolev embeddings together with a refined sub- and supersolution construction. Our arguments rely on monotone operator theory, which, combined with this framework, allows us to establish new existence results for this class of problems.