Search

In this paper, we use a new technique for the treatment of systems based on the advantage of vector-valued norms and of the weak topology. We first present vector versions of the Leray-Schauder alternative and then some Krasnoselskii type fixed point theorems for a sum of two mappings. Applications are given to a system of nonlinear transport equations, and systems of mixed fractional differential equations. [ABSTRACT FROM AUTHOR]

In this paper we discuss some topological properties of the set F(S0, T,z):= {x ∊ X : S0 x ∊ Tx + zg, where T is a nonlinear multi-valued mappings and S0 is a single-valued mappings acting on a Banach space X. This study is based on a new concept, the so called weakly relative demicompactness for nonlinear operators. [ABSTRACT FROM AUTHOR]

In this paper, using the technique of measure of weak noncompacteness, we prove some fixed set results of Krasnosel'skii type for the sum of two multivalued operators in the setting of weak topology, without the assumption of the convexity of their common domain. Applications to the theory of self-similarity are also given. [ABSTRACT FROM AUTHOR]