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

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.