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Zbl 1165.45010
Tidke, Haribhau L.
Existence of global solutions to nonlinear mixed Volterra-Fredholm integrodifferential equations with nonlocal conditions. (English)
[J] Electron. J. Differ. Equ. 2009, Paper No. 55, 7 p., electronic only (2009). ISSN 1072-6691/e

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 2000:: *45N05 Integral equations in abstract spaces
45G15 Systems of nonlinear integral equations
45J05 Integro-ordinary differential equations

Keywords: global solution; Leray-Schauder alternative; a priori bounds; nonlocal condition; nonlinear mixed Volterra-Fredholm integrodifferential equations; Banach spaces

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