## Journal of Integral Equations and Applications

### Global existence and asymptotic stability of mild solutions for stochastic evolution equations with nonlocal initial conditions

#### Abstract

The aim of this paper is to discuss the global existence, uniqueness and asymptotic stability of mild solutions for a class of semilinear evolution equations with nonlocal initial conditions on infinite interval. A sufficient condition is given for judging the relative compactness of a class of abstract continuous family of functions on infinite intervals. With the aid of this criteria the compactness of the solution operator for the problem studied on the half line is obtained. The theorems proved in this paper improve and extend some related results in this direction. Discussions are based on stochastic analysis theory, analytic semigroup theory, relevant fixed point theory and the well known Gronwall-Bellman type inequality. An example to illustrate the feasibility of our main results is also given.

#### Article information

Source
J. Integral Equations Applications, Volume 29, Number 2 (2017), 325-348.

Dates
First available in Project Euclid: 17 June 2017

https://projecteuclid.org/euclid.jiea/1497664831

Digital Object Identifier
doi:10.1216/JIE-2017-29-2-325

Mathematical Reviews number (MathSciNet)
MR3663526

Zentralblatt MATH identifier
1371.34086

#### Citation

Chen, Pengyu; Abdelmonem, Ahmed; Li, Yongxiang. Global existence and asymptotic stability of mild solutions for stochastic evolution equations with nonlocal initial conditions. J. Integral Equations Applications 29 (2017), no. 2, 325--348. doi:10.1216/JIE-2017-29-2-325. https://projecteuclid.org/euclid.jiea/1497664831

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