ON THE SOLUTIONS OF CERTAIN INTEGRAL-LIKE OPERATOR EQUATIONS, EXISTENCE, UNIQUENESS AND DEPENDENCE THEOREMS.
UNIVERSITY OF SOUTHERN CALIFORNIA LOS ANGELES ELECTRONIC SCIENCES LAB
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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
- Theoretical Mathematics