A generalization of Peano’s existence theorem and flow invariance

Michael G. Crandall

Type: Article

Publication Date: 1972-01-01

Citations: 56

DOI: https://doi.org/10.1090/s0002-9939-1972-0306586-2

Abstract

Let F£ R" be closed and A:F->-R" be continuous.Assuming that for y e F the distance from y+hAy to F is o(h) as AJO, it is shown that for each x 6 F the Cauchy problem u'=Au, u(0)=x, has a solution u: [0, Tx]->-Fon.some interval {0, Tx], Tx>0

Locations

Proceedings of the American Mathematical Society - View - PDF

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