Existence and Uniqueness of a Solution for a Non-Autonomous Semilinear Integro-Differential Equation With Deviated Argument

Existence and uniqueness of extremal mild solutions for non-autonomous nonlocal integro-differential equations via monotone iterative technique

“…Yan [20] studied the existence of mild solutions for non-autonomous integro-differential equations with nonlocal conditions by using the theory of evolution system, Banach contraction principle and Schauder's fixed point theorem. Haloi et al [11] studied existence, uniqueness and asymptotic stability of nonautonomous differential equations with deviated arguments via Banach fixed point theorem and theory of analytic semigroup. In [2], Alka et al established the existence and uniquenss of mild solutions for nonautonomous instantaneous impulsive differential equations with iterated deviating arguments by using analytic semigroup theory and Banach fixed point theorem.…”

Approximate Controllability of impulsive neutral integro-differential equations with deviated arguments and infinite delay in Banach spaces

“…For example, in automatic regulators, the delay is the interval of time, always present, which the system needs to react to the input impulse. The plentiful applications of differential equations with deviating arguments has motivated the rapid development of the theory of differential equations with deviating arguments and their generalization in the recent years see [13,14,16,19,26]. Extension of the theory of differential equations with deviating argument as well as stimuli of developments within various fields of science and technology contribute to the need for further development.…”

“…This theory in recent years has attracted the attention of vast number of researchers, interested in both in the theory and its applications. For more details, we refer [2,3,8,9,16,17] By the motivation of above mentioned literature we have proved the existence of mild solutions for an impulsive neutral integro-differential equation with infinite delay and with deviated argument in a Banach space (E, · ) through the utilization of the Schauder fixed point theorem. In section 2, we gave some definitions, preliminaries, some lemmas and theorems.…”

Monotone iterative technique for non-autonomous semilinear differential equations with nonlocal condition

“…The existence of mild solutions of a non-autonomous integro-differential equations with nonlocal conditions by using the theory of evolution families, Banach contraction principle and Schauder's fixed point theorem is studied by Yan [14]. Haloi et al [15] studied existence, uniqueness and asymptotic stability of non-autonomous differential equations with deviated arguments via Banach fixed point theorem and theory of analytic semigroup. In [16], Alka et al established the existence and uniquenss of mild solutions for non-autonomous instantaneous impulsive differential equations with iterated deviating arguments by using analytic semigroup theory and Banach fixed point theorem.…”