EXTENDED QUASILINEARIZATION METHOD FOR PERIODIC BOUNDARY VALUE PROBLEM OF FIRST ORDER DELAY DIFFERENTIAL EQUATIONS
By
Heramb Aiya1 and Y.S.Valaulikar2
1Research Student, 2Ex- Faculty, School of Physical and Applied Sciences, Goa University, Taleigaon Plateau, Goa, India-403206
Email: heramb.aiya@gmail.com, ysv@unigoa.ac.in ; valaulikarys@gmail.com
(Received: April 11, 2024; In format: April 20, 2024; Revised: November 02, 2024; Accepted: November 11, 2024)
DOI: https://doi.org/10.58250/jnanabha.2024.54220
Abstract
In this paper, we discuss the extended quasilinearization method to first order delay differential equation of the type x' (t) + λx(t) = f(t, x(t − r)) + g(t, x(t − r)) with periodic boundary conditions, where there are certain conditions on first and second order partial derivatives with respect to the second coordinate of f and g. The quasilinearization method helps us to find sequence of approximate solutions to non-linear problem, the limit of which, if exists, tends to a solution of the given non-linear problem.
2020 Mathematical Sciences Classification: 35F30, 34K10.
Keywords: Periodic Boundary Value Problem; Delay Differential Equation; Upper and Lower Solutions; Extended Quasilinearization.