An anisotropic Dirichlet system including unbounded coefficients

Dumitru Motreanu; Abdolrahman Razani; Elisabetta Tornatore

doi:10.3934/dcdss.2025015

Article Contents

2025, Volume 18, Issue 12: 3799-3817. Doi: 10.3934/dcdss.2025015

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An anisotropic Dirichlet system including unbounded coefficients

1.
Department of Mathematics, University of Perpignan, 66860 Perpignan, France
2.
Department of Pure Mathematics, Faculty of Science, Imam Khomeini International University, Postal code: 3414896818, Qazvin, Iran
3.
Department of Mathematics and Computer Science, University of Palermo, 90123 Palermo, Italy

^*Corresponding author: Dumitru Motreanu
^*Corresponding author: Dumitru Motreanu

Received: March 2024

Revised: January 2025

Early access: February 2025

Published: December 2025

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Abstract

This paper focuses on an anisotropic system driven by $ (p,q) $-Laplacian operators with unbounded coefficients depending on the solution, and whose lower order-terms exhibit full dependence on the solution and its gradient. The main results establish the existence of solutions and the uniform boundedness of the solution set. The approach is based on a suitable truncation to drop the unboundedness of the coefficients and on the solvability of the truncated system within the theory of pseudomonotone operators.

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Mathematics Subject Classification: Primary: 35P30, 35J60, 58B20, 35J20, 47J30; Secondary: 35J15, 35J70, 35J92.

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