EXISTENCE AND UNIQUENESS OF SOLUTIONS TO A WEIGHTED LAPLACE EQUATION WITH SPECTRAL PERTURBATION NEAR A PLANE SECTOR VERTEX

Hamza Medekhel, Rashid Jan, Salah Boulaaras (), Rafik Guefaifia () and Ahmed Himadan
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Hamza Medekhel: Laboratory of Operator Theory and EDP
Rashid Jan: Department of Mathematics, Saveetha School of Engineering (SIMATS), Thandalam, Chennai 600124, Tamil Nadu, India3Institute of Energy Infrastructure (IEI), Department of Civil Engineering College of Engineering, Universiti Tenaga Nasional (UNITEN), Putrajaya Campus, Jalan IKRAM-UNITEN, 43000 Kajang, Selangor, Malaysia
Salah Boulaaras: Department of Mathematics, College of Science, Qassim University, Buraydah 51452, Saudi Arabia
Rafik Guefaifia: Department of Mathematics, College of Science, Qassim University, Buraydah 51452, Saudi Arabia
Ahmed Himadan: Department of Mathematics, College of Science, Qassim University, Buraydah 51452, Saudi Arabia

FRACTALS (fractals), 2025, vol. 33, issue 08, 1-14

Abstract: This study investigates the stability and existence of periodic solutions in neutral differential systems with time delays and variable coefficients. Utilizing Krasnoselskii’s fixed point theorem, we demonstrate a set of sufficient conditions ensuring the existences of such a periodic solution. This involves transforming the system into an equivalent integral form before applying the fundamental matrix solutions alongside Floquet theory. In addition, we will analyze the asymptotic stability of these solutions, thus establishing new conditions that can ensure stability. The practical relevance of our theoretical results is supported through numerical examples, validating the proposed approach, and highlighting its suitability in areas such as electrical circuits, control systems, and biological modeling. This study extends previous work and thereby offers a detailed framework intended for use in studying neutral differential systems where time delays are present.

Keywords: Mathematical Model; Neutral Differential Systems; Periodic Solutions; Asymptotic Stability; Fixed Point Method (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1142/S0218348X25401784

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