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Existence of solutions for nonlinear mixed type integrodifferential equation of second order. (English) Zbl 1204.45015

The authors investigate the existence of solutions for nonlinear mixed Volterra-Fredholm integrodifferential equation of second order with nonlocal conditions in Banach spaces. The main tool used in this analysis is based on an application of the topological transversality theorem known as Leray-Schauder alternative, rely on a priori bounds of solutions and the inequality established by B. G. Pachpatte [Integral and finite difference inequalities and applications. North-Holland Mathematics Studies 205, Amsterdam: Elsevier (2006; Zbl 1104.26015)] . The interesting and useful aspect of the method employed here is that it yields simultaneously the global existence of solutions and the maximal interval of existence.

MSC:

45N05 Abstract integral equations, integral equations in abstract spaces
47B38 Linear operators on function spaces (general)
47H10 Fixed-point theorems

Citations:

Zbl 1104.26015
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