Abstract :
In this paper existence of extremal solutions of second order initial value problems with discontinuous right hand side is obtained under certain monotonicity conditions and without assuming the existence of upper and lower solutions. Two basic differential inequalities corresponding to these initial value problems are obtained in the form of extremal solutions. And also we prove uniqueness of solutions of given initial value problems under certain conditions. A. Sreenivas "Existence of Extremal Solutions of Second Order Initial Value Problems" Published in International Journal of Trend in Scientific Research and Development (ijtsrd), ISSN: 2456-6470, Volume-3 | Issue-4 , June 2019, URL: https://www.ijtsrd.com/papers/ijtsrd25192.pdf Paper URL: https://www.ijtsrd.com/mathemetics/other/25192/existence-of-extremal-solutions-of-second-order-initial-value-problems/a-sreenivas
Keyword :
Complete lattice, Tarski fixed point theorem, isotone increasing, minimal and maximal solutions