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<p>This paper investigates the existence of multiple weak solutions for a class of Kirchhoff-type fractional elliptic equations with Neumann boundary conditions, set in variable exponent fractional Sobolev spaces involving <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\varphi \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>φ</mi> </math></EquationSource> </InlineEquation>-Hilfer derivatives. By leveraging variational methods, key lemmas, and an extension of Ricceri’s theorem, we prove the presence of infinitely many solutions under nonstandard growth conditions. Examples are provided to illustrate the practical significance of these theoretical findings, contributing to the deeper analysis of Kirchhoff problems in fractional variable exponent frameworks.</p>

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On the multiplicity of solutions in fractional Kirchhoff-type problems with Neumann conditions

  • 期刊论文

  • 发表日期：

    2026年7月22日

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  • Mohamed El Khayr Boukraa,
  • Ahmed Ahmed,
  • Mohamed Saad Boukha Elemine Vall

摘要

This paper investigates the existence of multiple weak solutions for a class of Kirchhoff-type fractional elliptic equations with Neumann boundary conditions, set in variable exponent fractional Sobolev spaces involving \(\varphi \) φ -Hilfer derivatives. By leveraging variational methods, key lemmas, and an extension of Ricceri’s theorem, we prove the presence of infinitely many solutions under nonstandard growth conditions. Examples are provided to illustrate the practical significance of these theoretical findings, contributing to the deeper analysis of Kirchhoff problems in fractional variable exponent frameworks.