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Existence of mild solutions for fractional evolution equations with nonlocal initial conditions

Pengyu Chen, Yongxiang Li, Qiang Li (2014)

Annales Polonici Mathematici

This paper discusses the existence of mild solutions for a class of semilinear fractional evolution equations with nonlocal initial conditions in an arbitrary Banach space. We assume that the linear part generates an equicontinuous semigroup, and the nonlinear part satisfies noncompactness measure conditions and appropriate growth conditions. An example to illustrate the applications of the abstract result is also given.

Existence of mild solutions for semilinear equation of evolution

Anna Karczewska, Stanisław Wędrychowicz (1996)

Commentationes Mathematicae Universitatis Carolinae

The aim of this paper is to give an existence theorem for a semilinear equation of evolution in the case when the generator of semigroup of operators depends on time parameter. The paper is a generalization of [2]. Basing on the notion of a measure of noncompactness in Banach space, we prove the existence of mild solutions of the equation considered. Additionally, the applicability of the results obtained to control theory is also shown. The main theorem of the paper allows to characterize the set...

Existence of mild solutions on infinite intervals to first order initial value problems for a class of differential inclusions in banach spaces

Mouffak Benchohra (1999)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

In this paper we investigate the existence of mild solutions on an unbounded real interval to first order initial value problems for a class of differential inclusions in Banach spaces. We shall make use of a theorem of Ma, which is an extension to multivalued maps on locally convex topological spaces of Schaefer's theorem.

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