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Fractional evolution equation nonlocal problems with noncompact semigroups

Zhang X, Chen P.

Opuscula Mathematica

2016

Vol. 36, no. 1

123--137

This paper is concerned with the existence results of mild solutions to the nonlocal problem of fractional semilinear integro-differential evolution equations. New existence theorems are obtained by means of the fixed point theorem for condensing maps. The results extend and improve some related results in this direction.

Solving equations by topological methods

Górniewicz L.

Opuscula Mathematica

2005

Vol. 25, no. 2

195-225

In this paper we survey most important results from topological fixed point theory which can be directly applied to differential equations. Some new formulations are presented. We believe that our article will be useful for analysts applying topological fixed point theory in nonlinear analysis and in diffrential equations.

Fixed point theorems for admissible multivalued maps with nonconvex domains

Kim I.-S.

Bulletin of the Polish Academy of Sciences. Mathematics

2002

Vol. 50, no 4

457-467

Using the fixed point property of acyclic absolute neighbourhood retract due to L. Górniewicz, we prove that every compact admissible multivalued selfmap defined on an admissible pseudoconvex subset of a topological vector space has a fixed point.