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

Kholoud Saad Albalawi, Nadiyah Hussain Alharthi and Francesca Vetro
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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
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
Francesca Vetro: Independent Researcher, 90123 Palermo, Italy

Mathematics, 2022, vol. 10, issue 8, 1-15

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.

Keywords: Lebesgue and Sobolev spaces with variable exponents; parametric problems; gradient dependent term; Nemitsky map; pseudomonotone operator (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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