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Existence of global solutions to nonlinear mixed Volterra-Fredholm integrodifferential equations with nonlocal conditions. (English) Zbl 1165.45010
Summary: We investigate the existence of global solutions to first-order initial-value problems, with nonlocal condition for nonlinear mixed Volterra-Fredholm integrodifferential equations in Banach spaces. The technique used in our analysis is based on an application of the topological transversality theorem known as Leray-Schauder alternative and rely on a priori bounds of the solutions.
MSC:
45N05Abstract integral equations, integral equations in abstract spaces
45G15Systems of nonlinear integral equations
45J05Integro-ordinary differential equations