Remarks on Nonlocal Dirichlet Problems

Kholoud Saad Albalawi, Mona Bin-Asfour 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
Mona Bin-Asfour: 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 9, 1-14

Abstract: We study a nonlocal Dirichlet problem with the ( p ( b ( u ) ) , q ( b ( u ) ) ) -Laplacian operator and integrable data on a bounded domain with smooth boundary. We establish the existence of at least one weak solution in the case the variable exponents of the leading operator depend on the solution u , without assuming any growth conditions on g . The proof is based on the characterization of the energy functional associated to the problem, using the methods of the calculus of variations.

Keywords: ( p ( b ( u )), q ( b ( u )))-Laplacian operator; integrable data; nonlocal problem; nontrivial weak solution (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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