Optimality and existence for Lipschitz equations

[摘要] Solutions of certain boundary value problems are shown to exist for thenth order differential equationy(n)=f(t,y,y′,…,y(n−1)), wherefis continuous on a slab(a,b)×Rnandfsatisfies 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.

[学科分类] 数学（综合）