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Research Article | Open Access

A hyperbolic polyharmonic system in an exterior domain

Manal Alfulaij, Mohamed Jleli, Bessem Samet( )
Department of Mathematics, College of Science, King Saud University, Riyadh 11451, Saudi Arabia
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Abstract

A nonlinear hyperbolic polyharmonic system in an exterior domain of R N is considered under inhomogeneous Navier-type boundary conditions. Using nonlinear capacity estimates specifically adapted to the polyharmonic operator ( − Δ ) m , the geometry of the domain, and the boundary conditions, a sharp criterium for the nonexistence of weak solutions is obtained. Next, an optimal nonexistence result for the corresponding stationary problem is deduced.

Keywords

hyperbolic systemspolyharmonic operatorexterior domaininhomogeneous Navier-type boundary conditionsweak solutionsnonexistence
CLC number: 35A01, 35B33, 35L55, 31B30

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AIMS Mathematics
Volume 10 Issue 2,
February 2025
Pages 2634-2651
DOI: 10.3934/math.2025123

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Cite this article:
Alfulaij M, Jleli M, Samet B. A hyperbolic polyharmonic system in an exterior domain. AIMS Mathematics, 2025, 10(2): 2634-2651. https://doi.org/10.3934/math.2025123

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Received: 15 September 2024
Revised: 17 December 2024
Accepted: 23 December 2024
Published: 15 February 2025
©2025 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)