International Journal of Mathematics and Mathematical Sciences
Volume 11 (1988), Issue 2, Pages 267-274
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.
Solutions of certain boundary value problems are shown to exist for the th order differential equation , where is continuous on a slab and satisfies a Lipschitz condition on the slab. Optimal length subintervals of are determined, in terms of the Lipschitz coefficients, on which there exist unique solutions.