Regularity of solutions of Sobolev type semilinear integrodifferential equations in Banach spaces
Date
2003-11-20
Authors
Balachandran, Krishnan
Karunanithi, Subbarayan
Journal Title
Journal ISSN
Volume Title
Publisher
Southwest Texas State University, Department of Mathematics
Abstract
In this article, we prove the existence of mild and classical solutions of Sobolev type semilinear integrodifferential equations of the form
d/dt [Ex(t) = A[x(t) + ∫t0 F(t - s)x(s)ds] + ƒ(t, x(t))
in Banach spaces. The results are obtained by using the Banach contraction mapping principle and resolvent operator. An application is provided to illustrate the theory.
Description
Keywords
Classical solution, Semilinear integrodifferential equation, Resolvent operator, Fixed point theorem
Citation
Balachandran, K., & Karunanithi, S. (2003). Regularity of solutions of Sobolev type semilinear integrodifferential equations in Banach spaces. <i>Electronic Journal of Differential Equations, 2003</i>(114), pp. 1-8.
Rights
Attribution 4.0 International