Abstract.A theorem on the existence and continuous dependence upon initial-boundary conditions is given. The method of bicharacteristics is used to transform the mixed problem into a system of integral functional equations with operators of the Volterra type as a functional variable. A method of succesive approximations is used. The uniqueness of solutions of differential equation with the initial-boundary condition is proved by using a comparison technique. Classical solutions of integral functional equations lead to generalized solutions of the original problem. Differential equations with deviated variables and differential integral problems can be obtained from a general model by specializing given operators.

Received: May 16, 2006

AMS Subject Classification: 35F20, 39B22

Key Words and Phrases: functional differential equations, generalized solutions, comparison technique, method of succesive approximations, method of bicharacteristics

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2006
Volume: 29
Issue: 3