Jñānābha‎, Vol. 49 (2) (2019), 45-63

EXISTENCE AND ATTRACTIVITY THEOREMS FOR NONLINEAR FIRST ORDER HYBRID DIFFERENTIAL EQUATIONS WITH ANTICIPATION AND RETARDATION

By

Bapurao C. Dhage

"Kasubai", Gurukul Colony, Thodga Road, Ahmedpur - 413515, Dist. Latur, Maharashtra, India

Email:bcdhage@gmail.com

(Received : October 13, 2019 ; Revised: October 23, 2019)



Abstract

In this paper, we introduce the notion of a pulling function and establish an existence and global attractivity results for a nonlinear hybrid differential equation of quadratic type on the unbounded intervals of real line with mixed arguments of anticipations and retardations. A positivity result is also obtained under some usual natural conditions. The hybrid fixed point theoretic technology of Dhage (2004) is used while establishing our main results of the paper. Our hypotheses and claims have also been explained with the help of a natural realization.


2010 Mathematics Subject Classification34K10, 47H10.
Keywords and phrasesHybrid differential equation; Hybrid .xed point theorem; Existence theorem; Attractivity of solution.