Continuous Dependence of Solutions of Volterra Integral Equations.
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)
Document Details
- Document Type
- Technical Report
- Publication Date
- Aug 05, 1974
- Accession Number
- AD0785098
Entities
People
- Zvi Artstein
Organizations
- Brown University