On the Nonlinear Impulsive Volterra-Fredholm Integrodifferential Equations

Document Type : Research Paper

Authors

1 Department of Mathematics, Shivaji University, Kolhapur-416 004, Maharashtra, India.

2 Shivaji University, Kolhapur.

3 Department of Applied Mathematics, Imecc-Unicamp, 13083-859, Campinas, SP, Brazil.

Abstract

In this paper, we investigate existence and uniqueness of solutions of nonlinear Volterra-Fredholm impulsive integrodifferential equations. Utilizing theory of Picard operators we examine data dependence of solutions on initial conditions and on nonlinear functions involved in integrodifferential equations. Further, we extend the integral inequality for piece-wise continuous functions to mixed case and apply it to investigate the dependence of solution on initial data through $\epsilon$-approximate solutions. It is seen that the uniqueness and dependency results got by means of integral inequity requires less restrictions on the functions involved in the equations than that required through Picard operators theory.

Keywords