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<p>This paper is devoted to demonstrating several multiplicity results of nontrivial weak solutions to double phase problems of Kirchhoff type with Hardy potentials. The main features of the paper are the appearance of non-local Kirchhoff coefficients and the Hardy potential, the absence of the compactness condition of Palais-Smale, and the <i>L</i><sup>∞</sup>-bound for any possible weak solution. To establish multiplicity results, we utilize the fountain theorem and the dual fountain theorem as main tools. Also, we give the <i>L</i><sup>∞</sup>-bound for any possible weak solution by exploiting the De Giorgi iteration method and a truncated energy technique. As an application, we give the existence of a sequence of infinitely many weak solutions converging to zero in <i>L</i><sup>∞</sup>-norm. To derive this result, we employ the modified functional method and the dual fountain theorem.</p>

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On Kirchhoff-Hardy type problems involving double phase operators

  • 期刊论文

  • 发表日期：

    2025年6月20日

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  • Yun-Ho Kim,
  • Taek-Jun Jeong,
  • Jun-Yeob Shim

摘要

This paper is devoted to demonstrating several multiplicity results of nontrivial weak solutions to double phase problems of Kirchhoff type with Hardy potentials. The main features of the paper are the appearance of non-local Kirchhoff coefficients and the Hardy potential, the absence of the compactness condition of Palais-Smale, and the L∞-bound for any possible weak solution. To establish multiplicity results, we utilize the fountain theorem and the dual fountain theorem as main tools. Also, we give the L∞-bound for any possible weak solution by exploiting the De Giorgi iteration method and a truncated energy technique. As an application, we give the existence of a sequence of infinitely many weak solutions converging to zero in L∞-norm. To derive this result, we employ the modified functional method and the dual fountain theorem.