In this paper we study the existence of solutions for a system of upper semicontinuous, non necessarily convex, multivalued maps defined in abstract spaces. To this aim, we investigate the properties of the solution set of a multivalued equation. In particular we give conditions assuring the admissibility or the acyclicity of this map. The main tool is a technique to investigate fixed points of fiber-preserving maps. Some applications to boundary value problems for multivalued differential equations and for delay equations, are given.
On the solvability of systems of non-convex inclusions in Banach spaces / G. Conti; W. Kryszewski; P. Zecca. - In: ANNALI DI MATEMATICA PURA ED APPLICATA. - ISSN 0373-3114. - STAMPA. - 160 n.1:(1991), pp. 371-408. [10.1007/BF01764135]
On the solvability of systems of non-convex inclusions in Banach spaces
CONTI, GIUSEPPE;ZECCA, PIETRO
1991
Abstract
In this paper we study the existence of solutions for a system of upper semicontinuous, non necessarily convex, multivalued maps defined in abstract spaces. To this aim, we investigate the properties of the solution set of a multivalued equation. In particular we give conditions assuring the admissibility or the acyclicity of this map. The main tool is a technique to investigate fixed points of fiber-preserving maps. Some applications to boundary value problems for multivalued differential equations and for delay equations, are given.I documenti in FLORE sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.