Existence of mild solutions for abstract mixed type semilinear evolution equations

Authors: HONG-BO SHI, WAN-TONG LI, HONG-RUI SUN

Abstract: This paper is concerned with the existence of global mild solutions and positive mild solutions to initial value problem for a class of mixed type semilinear evolution equations with noncompact semigroup in Banach spaces. The main method is based on a new fixed point theorem with respect to convex-power condensing operator.

Keywords: Semilinear evolution equation; convex-power condensing operator; fixed point theorem; C_0-semigroup; measure of noncompactness

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