A class of BVPS for first order impulsive integro-differential equations

Abstract

In this paper, we study the impulsive integro-differential equations u ′ ( t ) = f ( t , u ( t ) , Tu , Su ) , t ≠ t k , t ∈ J = [ 0 , 1 ] , Δ u ( t k ) = I k ( u ( t k ) ) , k = 1 , 2 , … , m , u ( 0 ) = au ( 1 ) + bu ( ξ ) . The existence of maximal and minimal solutions to the problem is proved by using an upper and lower solutions method together with monotone iterative technique. And two monotone sequences which uniformly converge to the relevant solutions are obtained. An example is included to show the applicability of our results.