On certain classes of functional inclusions with causal operators in Banach spaces

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• 作者：Valeri Obukhovskii^a ; ^{valerio@math.vsu.ru} ; ; Pietro Zecca^b ; ^{zecca@unifi.it} ;
• 关键词：Causal operator ; Functional inclusion ; Cauchy problem ; Functional differential inclusion ; Volterra integro-differential inclusion ; Continuous dependence ; Measure of noncompactness ; Fixed point ; Topological degree ; Multivalued map ; Condensing map
• 刊名：Nonlinear Analysis
• 出版年：2011
• 出版时间：May 2011
• 年：2011
• 卷：74
• 期：8
• 页码：2765-2777
• 全文大小：276 K

文摘

We introduce the notion of a multivalued causal operator and consider an abstract Cauchy problem in a Banach space for various classes of functional inclusions with causal operators. The methods of the topological degree theory for condensing maps are applied to obtain local and global existence results for this problem and to study the continuous dependence of a solution set on initial data. As application we generalize some existence results for semilinear functional differential inclusions and Volterra integro-differential inclusions with delay.