Existence of Solutions of Quasilinear Integrodifferential Evolution Equations in Banach Spaces

Abstract

Abstract. We prove the local existence of classical solutions of quasilinear integrodifferential equations in Banach spaces. The results are obtained by using fractional powers of operators and the Schauder fixedpoint theorem. An example is provided to illustrate the theory.

Existence Results on General Integrodifferential Evolution Equations in Banach Space

“…The purpose of this paper is to prove the existence of mild solutions for time varying delay integrodifferential evolution equations with the help of Schaefer's fixed point theorem. The results generalize the results of [14].…”

Regularity of Solutions of Quasilinear Delay Integrodifferential Equations

“…Here a, b : I → I are real-valued continuous functions, k: I × X × X → X, α, β, γ : I → I are absolutely continuous functions. The equations considered in [1,11,13,20,21] are particular cases of the equation (1)-(2) and generalize the results of [3,4,12,14,15,20].…”

“…Balachandran and Uchiyama [5] discussed the existence and uniqueness of local mild and classical solutions of quasilinear integrodifferential equations. Recently Balachandran and Park [3] studied the existence of solutions of quasilinear integrodifferential evolution equations by using the Schauder fixed point theorem.…”

Existence result for nonlinear neutral integrodifferential equations with distributed delays

“…Ferenc (2003) also used Schauder's fixed point theorem to prove an existence theorem for Volterra integrodifferential equations with infinite delays. Balachandran and Kumer (2007) used the resolvent operator and Schaefer fixed point theorem to prove the existence of mild solutions of nonlinear integrodifferential equations with time varying delays in Banach space. Further in Balachandran and Shija (2004) a set of sufficient conditions for the existence of mild solutions of nonlinear neutral integrodifferential equations in Banach space were established.…”