Accession Number : AD0785098

Title :   Continuous Dependence of Solutions of Volterra Integral Equations.

Descriptive Note : Interim rept.,

Corporate Author : BROWN UNIV PROVIDENCE R I DIV OF APPLIED MATHEMATICS

Personal Author(s) : Artstein,Zvi

Report Date : 05 AUG 1974

Pagination or Media Count : 31

Abstract : The nonlinear Volterra integral equation is considered. The author discusses topologies on the collection of functions g such that the solution of the equation varies continuously with the data g and f, where the topology on f is the uniform convergence on compact intervals. A necessary and sufficient condition (on such a topology) for the continuous dependence to hold is given. In a particular case where a Lipschitz condition is added, it is shown that there exists a smallest topology which satisfies the condition. (Modified author abstract)

Descriptors :   *Volterra equations, *Topology, Differential equations, Inequalities, Theorems, Convergence

Subject Categories : Theoretical Mathematics

Distribution Statement : APPROVED FOR PUBLIC RELEASE