Summary
A uniqueness theorem by W. Walter for a second order Goursat problem in to independent variables is generalized. In the resulting theorem there are no restrictions on the order or on the number of indipendent variables.
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References
J. H. George,On Okamura's uniqueness theorem, Proc. Am. Math. Soc., 18, 764–765 (1967).
R. D. Moyer,A general uniqueness theorem, Proc. Am. Math. Soc., 17, 602–607 (1966).
M. Nagumo,Eine hinreichende Bedingung für die Unität der Lösung von Differentialgleichungen erster Ordning, Jap. J. Math., 3, 107–112 (1926).
H. Okamura Condition nécessaire et sufficiante remplie par les équations différentielles ordinaire sans points de Peano, Mem. Coll. Sci. Kyoto Univ, A 24, 21–28 (1942).
J. Persson,New proofs and generalizations of two theorems by Lednev for Goursat problems, Math. Ann., 178, 184–208 (1968).
—— ——,Exponential majorization and global Goursat problems, Math. Ann., 178, 271–276 (1968).
-- --,An existence theorem for a general Goursat problem, J. Diff. Eq. 5, 761–469.
-- --,Non-characteristic Cauchy problems and generalized Goursat problems in Rn, To appear in J. Math. and Mech.
W. Walter,Eindeutigkeitssätze für gewöhnliche, parabolische und hyperbolische Differentialgleichungen, Math. Z., 74, 191–208 (1960).
T. Yoshizawa,Stability theory by Liapunov's second method. The Math. Society of Japan, Tokyo, 1966.
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Entrata in Redazione il 17 ottobre 1968.
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Persson, J. Uniqueness and Goursat problems. Annali di Matematica 82, 173–182 (1969). https://doi.org/10.1007/BF02410796
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DOI: https://doi.org/10.1007/BF02410796