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<p>This paper investigates the multiplicity of solutions for a double phase problem involving a critical Choquard nonlinearity. The presence of the critical exponent <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(p^*_\mu \)</EquationSource> </InlineEquation>, which differs substantially from the usual critical exponent <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(p^*\)</EquationSource> </InlineEquation>, introduces some challenges in the analysis of the associated energy functional. By employing truncation techniques and genus theory, we establish the existence of infinitely many weak solutions with negative energy levels for the parameter <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(\lambda \in (0,\lambda ^*)\)</EquationSource> </InlineEquation>.</p>

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Multiplicity of solutions for a class of critical Choquard double phase problems

  • 期刊论文

  • 发表日期：

    2025年10月22日

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  • Qiyu Ren,
  • Yulin Zhao

摘要

This paper investigates the multiplicity of solutions for a double phase problem involving a critical Choquard nonlinearity. The presence of the critical exponent \(p^*_\mu \) , which differs substantially from the usual critical exponent \(p^*\) , introduces some challenges in the analysis of the associated energy functional. By employing truncation techniques and genus theory, we establish the existence of infinitely many weak solutions with negative energy levels for the parameter \(\lambda \in (0,\lambda ^*)\) .