Abstract
Various criteria are known for assuring uniqueness of the solution of a system ofn ordinary differential equations,x′ = f(t, x), with initial conditionx(t 0) = x0. Most of these involve some sort of relaxed Lipschitz condition onf(t, x), with respect tox, valid on an open setD ⊂ R 1+n which contains the point (t 0, x0). The present paper generalizes (and unifies) a number of known uniqueness criteria to cover cases when (t 0, x0) lies on the boundary ofD.
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Research partially supported by NSF Grant GP-37838.
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Bernfeld, S.R., Driver, R.D. & Lakshmikantham, V. Uniqueness for ordinary differential equations. Math. Systems Theory 9, 359–367 (1975). https://doi.org/10.1007/BF01715361
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DOI: https://doi.org/10.1007/BF01715361