International Journal of Mathematics and Mathematical Sciences
Volume 11 (1988), Issue 2, Pages 267-274
doi:10.1155/S0161171288000328
Optimality and existence for Lipschitz equations
Department of Algebra, Combinatorics & Analysis, Auburn University, Auburn, Alabama 36849, USA
Received 5 January 1987; Revised 28 July 1987
Copyright © 1988 Johnny Henderson. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract
Solutions of certain boundary value problems are shown to exist for the nth order differential equation y(n)=f(t,y,y′,…,y(n−1)), where f is continuous on a slab (a,b)×Rn and f satisfies a Lipschitz condition on the slab. Optimal length subintervals of (a,b) are determined, in terms of the Lipschitz coefficients, on which there exist unique solutions.