Singular Quadratic Functionals and Second Order Matrix Differential Equations.
Final rept. 1 Jul 68-30 Jun 72,
CONNECTICUT UNIV STORRS
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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 Pt 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 RtX PtX 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
- Theoretical Mathematics