Accession Number:

AD0701068

Title:

ON THE SOLUTIONS OF CERTAIN INTEGRAL-LIKE OPERATOR EQUATIONS, EXISTENCE, UNIQUENESS AND DEPENDENCE THEOREMS.

Descriptive Note:

Research rept.,

Corporate Author:

UNIVERSITY OF SOUTHERN CALIFORNIA LOS ANGELES ELECTRONIC SCIENCES LAB

Personal Author(s):

• Neustadt,Lucien W.

Report Date:

1970-02-01

Pagination or Media Count:

58.0

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

Descriptors:

• (*FUNCTIONAL ANALYSIS
• *DIFFERENTIAL EQUATIONS)
• (*INTEGRAL EQUATIONS
• THEOREMS)
• VECTOR SPACES
• CONVEX SETS
• TOPOLOGY

Subject Categories:

• Theoretical Mathematics

Distribution Statement:

APPROVED FOR PUBLIC RELEASE