Nonlinear Integrodifferential Equations with Time Varying Delay

Rakesh KUMAR, Kamlendra KUMAR, Manoj KARNATAKA
2021 Advances in the Theory of Nonlinear Analysis and its Applications  
By practicing the manner of semigroup theory and Banach contraction theorem, the existence and uniqueness of mild and classical solutions of nonlinear integrodierential equations with time varying delay in Banach spaces is showed. Certainly, an example is revealed to justify the abstract idea. If Ω = 0 then T (t) is called uniformly bounded and if M = 1 it is said to be C 0 -semigroup of contraction. Now, if E is assumed as a Banach space with norm . . Also, C 0 -semigroup of operators on E is
more » ... ritten by {T (t)} t≥0 . Throughout paper, innitesimal generator is represented by −A and the same is C 0 -semigroup of operators on E. Here the domain of A is given by D(A) and also t 0 ≥ 0, b > 0,
doi:10.31197/atnaa.814109 fatcat:5vo7mbm2snfilafsjsobqfqvvu