
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