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<p>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.</p>

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

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年10月7日

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  • Rafik Guefaifia,
  • Salah Boulaaras,
  • Abdelaziz Sabiry

摘要

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.