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Existence theorems of global solutions of initial value problems for nonlinear integrodifferential equations of mixed type in Banach spaces and applications. (English) Zbl 1050.45003
This paper deals with the existence of global solutions for some mixed integrodifferential equations with initial value in a Banach space. The authors use the Kuratowski measure of noncompactness of sets and the Schauder fixed point theorem in order to prove the existence of global solutions. Finally they propose to study the existence of global solutions for two classes of third order mixed boundary value problem.
MSC:
45N05Abstract integral equations, integral equations in abstract spaces
45J05Integro-ordinary differential equations
45G10Nonsingular nonlinear integral equations
47H09Mappings defined by “shrinking” properties