A Nagumo condition for ordinary differential equations

Jackson, L. K.

doi:10.1090/S0002-9939-1976-0404761-3

A Nagumo condition for ordinary differential equations

Author: L. K. Jackson
Journal: Proc. Amer. Math. Soc. 57 (1976), 93-96
MSC: Primary 34C10
DOI: https://doi.org/10.1090/S0002-9939-1976-0404761-3
MathSciNet review: 0404761
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: A condition is given which guarantees that each solution of ${y^{(n)}} = f(x,y,y', \ldots ,{y^{(n - 1)}})$ either extends or becomes unbounded on its maximal interval of existence.

[1] P. Hartman, Ordinary differential equations, Wiley, New York and London, 1964. MR 30 #1270. MR 0171038 (30:1270)
[2] L. K. Jackson, Subfunctions and second-order differential inequalities, Advances in Math. 2 (1968), 307-363. MR 37 #5462. MR 0229896 (37:5462)
[3] K. W. Schrader, Existence theorems for second order boundary value problems, J. Differential Equations 5 (1969), 572-584. MR 39 #532. MR 0239175 (39:532)
[4] G. A. Klaasen, Differential inequalities and existence theorems for second and third order boundary value problems, J. Differential Equations 10 (1971), 529-537. MR 44 #5595. MR 0288397 (44:5595)
[5] W. G. Kelley, Some existence theorems for th-order boundary value problems, J. Differential Equations 18 (1975), 158-169. MR 0367351 (51:3593)
[6] J. Bebernes, R. Gaines and K. Schmitt, Existence of periodic solutions for third and fourth order ordinary differential equations via coincidence degree, Ann. Soc. Sci. Bruxelles Sér. I 88 (1974), 25-36. MR 49 #5480. MR 0340729 (49:5480)
[7] A. Gorny, Contribution à l'étude des fonctions dérivables d'une variable réelle, Acta Math. 71 (1939), 317-358. MR 1, 137; 400. MR 0000848 (1:137d)