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<p>In this paper, we deal with a new kind of elliptic competing inclusions which involve variable exponent double-phase operators with logarithmic perturbation, nonlocal terms, mixed boundary conditions and multivalued convection terms. We here establish a new framework for determining the existence of generalized solutions and strongly generalized solutions to such type of problems. Our results extend the recent ones by Cen–Marano–Zeng (Appl Math Lett 167:109556, 2025).</p>

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Existence of generalized solutions to a new kind of elliptic systems with variable exponent double-phase competing operators

  • 期刊论文

  • 发表日期：

    2026年1月7日

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  • Guangwang Su,
  • Francesca Vetro,
  • Boling Chen

摘要

In this paper, we deal with a new kind of elliptic competing inclusions which involve variable exponent double-phase operators with logarithmic perturbation, nonlocal terms, mixed boundary conditions and multivalued convection terms. We here establish a new framework for determining the existence of generalized solutions and strongly generalized solutions to such type of problems. Our results extend the recent ones by Cen–Marano–Zeng (Appl Math Lett 167:109556, 2025).