Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

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.


References [Enhancements On Off] (What's this?)

  • [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 $ n$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)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 34C10

Retrieve articles in all journals with MSC: 34C10


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1976-0404761-3
Keywords: Nagumo condition, maximal interval of existence, boundary value problem, differential inequalities
Article copyright: © Copyright 1976 American Mathematical Society

American Mathematical Society