Existence of global solutions to nonlinear mixed Volterra-Fredholm integrodifferential equations with nonlocal conditions

Abstract

In this paper, 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 solution.

Keywords

• Global solution
• Volterra-Fredholm integrodifferential equation
• Leray-Schauder alternative
• priori bounds
• nonlocal condition