Optimality and existence for Lipschitz equations

Johnny Henderson

International Journal of Mathematics and Mathematical Sciences, 1988, vol. 11, 1-8

Abstract:

Solutions of certain boundary value problems are shown to exist for the n th order differential equation y ( n ) = f ( t , y , y ′ , … , y ( n − 1 ) ) , where f is continuous on a slab ( a , b ) × R n 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.

Date: 1988
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:154362

DOI: 10.1155/S0161171288000328

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