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)



Perturbations causing oscillations of functional-differential equations

Authors: A. G. Kartsatos and M. N. Manougian
Journal: Proc. Amer. Math. Soc. 43 (1974), 111-117
MSC: Primary 34K15
MathSciNet review: 0328270
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: Some new criteria are given for the oscillation of solutions of perturbed functional-differential equations of the form

$\displaystyle ({\text{I}})\quad {x^{(n)}} + P(t)f(x(g(t))) = Q(t).$

The results are new even in the case $ g(t) \equiv t$, or when $ ({\text{I}})$ is linear. The function $ Q(t)$ does not have to be small or periodic.

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

  • [1] F. V. Atkinson, On second-order differential inequalities (to appear). MR 0402175 (53:5996)
  • [2] A. G. Kartsatos, A contribution to the investigation of the oscillations and asymptotic behavior of the solutions of ordinary differential equations, Bull. Soc. Math. Grèce 10 (1969), fasc. 2, 1-50, 135. (Greek) MR 43 #618. MR 0274860 (43:618)
  • [3] -, On the maintenance of oscillations of $ n$th order equations under the effect of a small forcing term, J. Differential Equations 10 (1971), 355-363. MR 44 #5556. MR 0288358 (44:5556)
  • [4] -, Maintenance of oscillations under the effect of a periodic forcing term, Proc. Amer. Math. Soc. 33 (1972), 377-383. MR 0330622 (48:8959)
  • [5] T. Kusano and H. Onose, Oscillations of functional differential equations with retarded arguments, J. Differential Equations (to appear). MR 0333398 (48:11723)
  • [6] H. Teufel Jr., Forced second order nonlinear oscillation, J. Math. Anal. Appl. 40 (1972), 148-152. MR 0313583 (47:2137)
  • [7] E. True, Doctoral Dissertation, Montana State University, Bozeman, Mt., 1972.

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 34K15

Retrieve articles in all journals with MSC: 34K15

Additional Information

Keywords: Oscillation of solutions, nonoscillation of solutions, bounded solutions, nonlinear differential equations
Article copyright: © Copyright 1974 American Mathematical Society

American Mathematical Society