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<p>In this paper, we study a bi-nonlocal elliptic problem involving the operator <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\(p(x)-\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>p</mi> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> <mo>-</mo> </mrow> </math></EquationSource> </InlineEquation>Laplacian. Applying variational methods (Mountain Pass Theorem-Krasnoselskii’s Genus) and under suitable conditions, we prove several results on the existence of positive solutions. To the best of our knowledge, this paper is one of the first contributions to the study of bi-nonlocal elliptic problem with dependence on the Gradient.</p>

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On a bi-nonlocal \(p(x)-\)Kirchhoff equation with dependence on the gradient via mountain pass techniques

  • 期刊论文

  • 发表日期：

    2025年6月9日

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  • A. Zaki,
  • N. Tsouli,
  • H. Baladi,
  • A. Aglzim

摘要

In this paper, we study a bi-nonlocal elliptic problem involving the operator \(p(x)-\) p ( x ) - Laplacian. Applying variational methods (Mountain Pass Theorem-Krasnoselskii’s Genus) and under suitable conditions, we prove several results on the existence of positive solutions. To the best of our knowledge, this paper is one of the first contributions to the study of bi-nonlocal elliptic problem with dependence on the Gradient.