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Vol. 49 No. 4 (2023)
Serdica Mathematical Journal

Articles

Monotone iterative method for boundary value problem with linear condition of first order delay differential equation

https://doi.org/10.55630/serdica.2023.49.283-300

Published 21-12-2023

  • Heramb Aiya
    • ,
  • Yeshwant Shivrai Valaulikar

Heramb Aiya
Goa University

Yeshwant Shivrai Valaulikar
Goa University

Abstract

In this paper we discuss the boundary value problem for a first order delay differential equation of the type, \(y'(t) + \lambda y(t) = f(t, y(t - r))\). We prove the existence of solution between weakly coupled lower and upper solution by assuming \(f\) to be a non-decreasing function in the second coordinate. Further, we use this existence result to establish monotone iterative method, where we obtain increasing as well as decreasing sequence of functions whose limits are a solution of the boundary value problem. The sequence of functions obtained are solutions of some defined boundary value problem with linear condition of linear delay differential equation.

2020 Mathematics Subject Classification:

34B15, 34C25, 34K05, 34K10

Keywords

boundary value problem, delay differential equation, weakly coupled lower and upper solution, monotone iterative method

Full text

Author Details

Heramb Aiya

School of Physical and Applied Sciences
Goa University
Taleigao Plateau – Goa – India, 403206
e-mail: heramb.aiya@gmail.com

Yeshwant Shivrai Valaulikar

Department of Mathematics
Goa University
Taleigao Plateau – Goa – India, 403206
e-mail: ysv@unigoa.ac.in, valaulikarys@gmail.com

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