Existence of mild solutions for abstract mixed type semilinear evolution equations

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.

Anahtar Kelimeler:

Semilinear evolution equation; convex-power condensing operator; fixed point theorem; C0-semigroup; measure of noncompactness

Existence of mild solutions for abstract mixed type semilinear evolution equations

Keywords:

Semilinear evolution equation; convex-power condensing operator; fixed point theorem; C0-semigroup; measure of noncompactness,

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Hong—Bo SH11’2, Wan-Tong LIM, Hong—Rui SUNl Received: 27.05.2009
School of Mathematics and Statistics, Lanzhou University, Lanzhou, Gansu 730000,
People’s Republic of CHINA *Corresponding author {e—mail: wtli©lzu.edu.cn} School of Mathematical Science, Huaiyin Normal University, Huaian, Jiangsu 223300,
People’s Republic of CHINA