Mixed Monotone Iterative Technique for Abstract Impulsive Evolution Equations in Banach Spaces
نویسندگان
چکیده
Impulsive differential equations are a basic tool for studying evolution processes of real life phenomena that are subjected to sudden changes at certain instants. In view of multiple applications of the impulsive differential equations, it is necessary to develop the methods for their solvability. Unfortunately, a comparatively small class of impulsive differential equations can be solved analytically. Therefore, it is necessary to establish approximation methods for finding solutions. The monotone iterative technique of Lakshmikantham et al. see 1–3 is such a method which can be applied in practice easily. This technique combines the idea of method of upper and lower solutions with appropriate monotone conditions. Recent results by means of monotone iterative method are obtained in 4–7 and the references therein. In this paper, by using a mixed monotone iterative technique in the presence of coupled lower and upper L-quasisolutions, we consider the existence of mild ωperiodic L-quasi solutions for the periodic boundary value problem PBVP of impulsive evolution equations
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