Geodesic
Remarks on the Uniqueness Theorem of Solutions of the Darboux Problem
Canadian mathematical bulletin, Tome 8 (1965) no. 6, pp. 791-796

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Recently B. Palczewski and W. Pawelski [l] have given some sufficient conditions of uniqueness for the solutions of the Darboux problem for equations of the form: 1 The criteria given there for equations of the form (1) are natural generalizations of the criteria given by Krasnosielski and Krein [2] in the corresponding ordinary differential case. The purpose of the present note is to give a further generalization of the above result and two other uniqueness conditions for the solutions of the Darboux problem of the same form. 
Wong, James S. W. Remarks on the Uniqueness Theorem of Solutions of the Darboux Problem. Canadian mathematical bulletin, Tome 8 (1965) no. 6, pp. 791-796. doi: 10.4153/CMB-1965-059-1
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[1] 1. Palczewski, B. and Pawelski, W., Some remarks on the uniqueness of solutions to the Darboux problem with conditions of the Krasnosielski-Krein type, Ann. Polon. Math. XIV (1964), pp. 97-100. Google Scholar

[2] 2. Krasnosielski, M. A. and Krein, S. G., On a class of uniqueness theorems for the equation y' = f(x, y), Uspehi Mat. Nauk. (N.S.)11 (1956), No.1 (67), 209-213. Google Scholar

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[5] 5. Nagumo, M., Eine hinreichende Bedingung für die Unität der Lösung von Differentialgleichungen erster Ordnung, Japan J. Math. 3 (1926) pp. 107-112. Google Scholar

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