ON THE SOLUTIONS OF CERTAIN INTEGRAL-LIKE OPERATOR EQUATIONS, EXISTENCE, UNIQUENESS AND DEPENDENCE THEOREMS.
Abstract
Equations of the form x = Tx are studied, where x is a continuous, finite-dimensional vector-valued function defined on a compact interval, and T is an operator from a set in the linear space of all such functions into this space. Under suitable assumptions - which essentially assert that the operator T is, in some sense, integral-like--local existence, continuation and uniqueness theorems are proved, which are very analogous to those for ordinary differential equations. Further theorems are proved covering the dependence of x on T which generalize well-known continuous and differentiable dependence theorems for ordinary differential equations. The general results are applied to ordinary differential equations, Volterra integral equations, and functional differential equations. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Feb 01, 1970
- Accession Number
- AD0701068
Entities
People
- Lucien W. Neustadt
Organizations
- University of Southern California