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<p>In this paper, we focus on a Dirichlet problem defined by a system of equations driven by multi-phase operators with variable exponents. Such equations have a right side which depends on the gradient of the solutions. Under very general assumptions on the nonlinearities, we first establish an existence and localization result for the problem under consideration via sub-supersolution method. Then, we produce constant sign solutions, that is, whose components are both positive or both negative.</p>

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Variable exponent multi-phase problems: existence and localization results via sub-supersolution method

  • 期刊论文

  • 发表日期：

    2025年12月27日

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  • Francesca Vetro,
  • Rakib Efendiev

摘要

In this paper, we focus on a Dirichlet problem defined by a system of equations driven by multi-phase operators with variable exponents. Such equations have a right side which depends on the gradient of the solutions. Under very general assumptions on the nonlinearities, we first establish an existence and localization result for the problem under consideration via sub-supersolution method. Then, we produce constant sign solutions, that is, whose components are both positive or both negative.