Accession Number : AD0697740

Title :   EXISTENCE AND UNIQUENESS OF SOLUTIONS OF BOUNDARY VALUE PROBLEMS FOR SECOND ORDER SYSTEMS OF NONLINEAR DIFFERENTIAL EQUATIONS.

Corporate Author : IOWA UNIV IOWA CITY DEPT OF MATHEMATICS

Personal Author(s) : Waltman,Paul

Report Date : MAR 1969

Pagination or Media Count : 31

Abstract : Questions of the existence and uniqueness of solutions of the two point boundary value problem y double prime + f)t,y,y') = O, y(a) = A, y(b) = B, where f(t,y,y') satisfies a Lipschitz condition, have a long history, agoing back to Picard, 1893. The problem is to determine, in terms of the Lipschitz constants, the best possible interval (a,b) on which there exists a unique solution of these equations. A second question of interest is, given that solutions of these equations are unique, i.e., given that there exists at most one solution, when does this imply that there exists at least one solution. This paper investigates these two types of questions for the second order system, x' = f sub 1 (t,x,y), y' = f sub 2 (t,x,y), subject to more general boundary conditions g sub 1 (x(a),y(a)) = c sub 1, g sub 2 (x(b),y(b)) = c sub 2. (Author)

Descriptors :   (*NONLINEAR DIFFERENTIAL EQUATIONS, *BOUNDARY VALUE PROBLEMS), PARTIAL DIFFERENTIAL EQUATIONS, BOUNDARY VALUE PROBLEMS, THEOREMS

Subject Categories : Numerical Mathematics

Distribution Statement : APPROVED FOR PUBLIC RELEASE