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Gradient and Parameter Dependent Dirichlet ( p ( x ), q ( x ))-Laplace Type Problem

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  • Kholoud Saad Albalawi

    (Department of Mathematics and Statistics, College of Science, Imam Mohammad Ibn Saud Islamic University, P.O. Box 90950, Riyadh 11623, Saudi Arabia
    These authors contributed equally to this work.)

  • Nadiyah Hussain Alharthi

    (Department of Mathematics and Statistics, College of Science, Imam Mohammad Ibn Saud Islamic University, P.O. Box 90950, Riyadh 11623, Saudi Arabia
    These authors contributed equally to this work.)

  • Francesca Vetro

    (Independent Researcher, 90123 Palermo, Italy
    These authors contributed equally to this work.)

Abstract

We analyze a Dirichlet ( p ( x ) , μ q ( x ) ) -Laplace problem. For a gradient dependent nonlinearity of Carathéodory type, we discuss the existence, uniqueness and asymptotic behavior of weak solutions, as the parameter μ varies on the non-negative real axis. The results are obtained by applying the properties of pseudomonotone operators, jointly with certain a priori estimates.

Suggested Citation

  • Kholoud Saad Albalawi & Nadiyah Hussain Alharthi & Francesca Vetro, 2022. "Gradient and Parameter Dependent Dirichlet ( p ( x ), q ( x ))-Laplace Type Problem," Mathematics, MDPI, vol. 10(8), pages 1-15, April.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:8:p:1336-:d:796096
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    Cited by:

    1. Mina Ghasemi & Calogero Vetro & Zhenfeng Zhang, 2025. "Dirichlet μ -Parametric Differential Problem with Multivalued Reaction Term," Mathematics, MDPI, vol. 13(8), pages 1-15, April.

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