Existence of solutions for nonlinear mixed type integrodifferential equation of second order

Abstract

In this paper, we investigate the existence of solutions for nonlinear mixed Volterra-Fredholm integrodifferential equation of second order with nonlocal conditions in Banach spaces. Our analysis is based on Leray-Schauder alternative, rely on a priori bounds of solutions and the inequality established by B. G. Pachpatte.

Keywords

• Volterra-Fredholm integrodifferential equation
• Leray-Schauder alternative
• Semigroup theory
• Priori bounds of solutions
• Nonlocal condition and Pachpatte's integral inequality