On a class of abstract fourth-order differential equations set on cusp domain

Naceur Cheghloufa\(^a\), Belkacem Chaouchi\(^{b,∗}\), Marko Kostic’\(^c\), Fatiha Boutaous\(^d\)

\(^a\)Department of Mathematics, Faculty of Sciences, Saad Dahlab University, 09000, Blida1, Algeria.

\(^b\)Department of Renewable Energy, University of Khemis Miliana, Khemis Miliana, 44225, Algeria.

\(^c\)Faculty of Technical Sciences, University of Novi Sad, Trg D. Obradovi ́ca 6, 21125, Novi Sad, Serbia.

\(^d\)Department of Mathematics, Faculty of Sciences, Saad Dahlab University, 09000, Blida1, Algeria.

Correspondence should be addressed to: chegloufa.naceur@etu.univ-blida.dz,chaouchicukm@gmail.com,

Copyright © 2025 Naceur Cheghloufa, Belkacem Chaouchi, Marko Kostic’, Fatiha Boutaous. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Published: Received: 22 November 2024; Accepted: 11 Januay 2025; Published Online: 24 January 2025

Abstract

In this work, we concentrate on a boundary value problem set on a singular domain containing a cuspidial point. In our study, we obtain some existence and maximal regularity results. Our strategy is based on the study of a boundary value problems for a class of the complete abstract fourth-order differential equations involving fractional powers of unbounded linear operators.

Keywords:

Cusp domains, abstract differential equations, Hilbert spaces, Sobolev spaces, fractional powers of operators.