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Turkish Journal of Mathematics

Existence of mild solutions for abstract mixed type semilinear evolution equations

Hong-Bo SHI1,2, Wan-Tong LI1*, Hong-Rui SUN1
1School of Mathematics and Statistics,
Lanzhou University,
Lanzhou, Gansu 730000,
People's Republic of CHINA
*e-mail: wtli@lzu.edu.cn
2School of Mathematical Science,
Huaiyin Normal University,
Huaian, Jiangsu 223300,
People's Republic of CHINA

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.

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

Turk. J. Math., 35, (2011), 457-472.
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Other articles published in the same issue: Turk. J. Math.,vol.35,iss.3.