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Keywords = (p,q)-Laplace differential inclusion

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15 pages, 280 KiB  
Article
Dirichlet μ-Parametric Differential Problem with Multivalued Reaction Term
by Mina Ghasemi, Calogero Vetro and Zhenfeng Zhang
Mathematics 2025, 13(8), 1295; https://doi.org/10.3390/math13081295 - 15 Apr 2025
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Abstract
We study a Dirichlet μ-parametric differential problem driven by a variable competing exponent operator, given by the sum of a negative p-Laplace differential operator and a positive q-Laplace differential operator, with a multivalued reaction term in the sense of a [...] Read more.
We study a Dirichlet μ-parametric differential problem driven by a variable competing exponent operator, given by the sum of a negative p-Laplace differential operator and a positive q-Laplace differential operator, with a multivalued reaction term in the sense of a Clarke subdifferential. The parameter μR makes it possible to distinguish between the cases of an elliptic principal operator (μ0) and a non-elliptic principal operator (μ>0). We focus on the well-posedness of the problem in variable exponent Sobolev spaces, starting with energy functional analysis. Using a Galerkin approach with a priori estimate and embedding results, we show that the functional associated with the problem is coercive; hence, we prove the existence of generalized and weak solutions. Full article
(This article belongs to the Section C: Mathematical Analysis)
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