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:

1974-08-05

Pagination or Media Count:

31.0

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