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Existence and Uniqueness of a Solution for a Non-Autonomous Semilinear Integro-Differential Equation With Deviated Argument

  • Rajib HaloiEmail author
  • Dwijendra N. Pandey
  • D. Bahuguna
Original Research

Abstract

In this paper, we consider a non-autonomous semilinear integro-differential equation of parabolic type with deviated argument in an arbitrary Banach space. Using the Sobolevskiĭ–Tanabe theory of parabolic equations, we prove the existence and uniqueness of a solution. As an application, we include an example to illustrate the theory.

Keywords

Analytic semigroup Parabolic equation Integro-differential equation with deviated argument Banach fixed point theorem 

Mathematics Subject Classification (2000)

34G20 34K30 35K90 

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Copyright information

© Foundation for Scientific Research and Technological Innovation 2011

Authors and Affiliations

  • Rajib Haloi
    • 1
    Email author
  • Dwijendra N. Pandey
    • 2
  • D. Bahuguna
    • 1
  1. 1.Department of Mathematics and StatisticsIndian Institute of Technology KanpurKanpurIndia
  2. 2.Department of MathematicsIndian Institute of Technology RoorkeeRoorkeeIndia

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