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<p>This paper investigates a class of double phase inclusion problems with variable exponents and mixed boundary conditions on bounded Lipschitz domains. The right-hand side of the problem involves both Clarke subdifferentials, describing nonconvex constraints, and convex subdifferentials, corresponding to convex constraints. By constructing a total functional associated with the problem that combines convex and locally Lipschitz components, and by applying Ekeland’s variational principle together with Yosida approximation techniques and subdifferential calculus, we establish the existence of nontrivial bounded weak solutions under suitable assumptions. Our results extend the ones established in [J. Differential Equations 316 (2022), 249-269].</p>

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Variable Exponent Mixed Double Phase Inclusions Under Nonconvex Constraints

  • 期刊论文

  • 发表日期：

    2026年7月17日

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  • Shengda Zeng,
  • Yasi Lu,
  • Patrick Winkert

摘要

This paper investigates a class of double phase inclusion problems with variable exponents and mixed boundary conditions on bounded Lipschitz domains. The right-hand side of the problem involves both Clarke subdifferentials, describing nonconvex constraints, and convex subdifferentials, corresponding to convex constraints. By constructing a total functional associated with the problem that combines convex and locally Lipschitz components, and by applying Ekeland’s variational principle together with Yosida approximation techniques and subdifferential calculus, we establish the existence of nontrivial bounded weak solutions under suitable assumptions. Our results extend the ones established in [J. Differential Equations 316 (2022), 249-269].