Accession Number : AD0765654

Title :   Singular Quadratic Functionals and Second Order Matrix Differential Equations.

Descriptive Note : Final rept. 1 Jul 68-30 Jun 72,

Corporate Author : CONNECTICUT UNIV STORRS

Personal Author(s) : Tomastik,Edmond C.

Report Date : 02 JUL 1973

Pagination or Media Count : 9

Abstract : A phase of the study of principal quadratic functionals of n dependent variables initiated in a previous paper is completed. Sufficient conditions for the existence of a minimum in the missing case in the previous paper are given. In addition the techniques given here are sufficiently general to not require the matrix P(t) to be positive definite, and to solve the variable end point problem also. Also a very general sufficient condition for the oscillation of the linear second order n x n matrix equation (R(t)X')' + P(t)X = O is given. Finally results for this last equation are given an asymptotic behavior generalizing the well known results of Hille for the scalar case. (Modified author abstract)

Descriptors :   (*DIFFERENTIAL EQUATIONS, MATRICES(MATHEMATICS)), VECTOR SPACES, THEOREMS, ASYMPTOTIC SERIES

Subject Categories : Theoretical Mathematics

Distribution Statement : APPROVED FOR PUBLIC RELEASE