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)



An oscillation criterion for a forced second order linear differential equation

Author: M. A. El-Sayed
Journal: Proc. Amer. Math. Soc. 118 (1993), 813-817
MSC: Primary 34C10
MathSciNet review: 1154243
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: The paper is devoted to an oscillation theorem for the second-order forced linear differential equation of the form $ (p(t)x')' + q(t)x = g(t)$. The sign of the coefficient $ q$ is not definite, and the function $ g$ is not necessarily the second derivative of an oscillatory function. The question raised by J. Wong in Second order nonlinear forced oscillations (SIAM J. Math. Anal. 19 (1988), 667-675) is answered. A region of oscillation of Mathieu's equation is specified.

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

  • [1] W. A. Coppel, Disconjugacy, Lecture Notes in Math., vol. 220, Springer-Verlag, Berlin, 1971. MR 0460785 (57:778)
  • [2] H. C Howard, Oscillation and nonoscillation criteria for nonhomogeneous differential equations, Ann. Mat. Pura Appl. (4) (1977), 163-180. MR 533605 (81c:34028)
  • [3] A. G. Kartsatos, On the maintenance of oscillation of nth order equations under the effect of a small forcing term, J. Differential Equations 10 (1971), 355-363. 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] W. Leighton, Comparison theorems for linear differential equations of second order, Proc. Amer Math. Soc. 13 (1962), 603-610. MR 0140759 (25:4173)
  • [6] W. T. Reid, A comparison theorem for self adjoint differential equations of second order, Ann. of Math. (2) 65 (1957), 195-202. MR 0092045 (19:1052b)
  • [7] C. A. Swanson, Comparison and oscillation theory of linear differential equations, Academic Press, New York, 1968. MR 0463570 (57:3515)
  • [8] E. T. Whittaker and G. N. Watson, A course of modern analysis, Cambridge Univ. Press, Cambridge and New York, 1965. MR 1424469 (97k:01072)
  • [9] J. S. W. Wong, Second order nonlinear forced oscillations, SIAM J. Math. Anal. 19 (1988), 667-675. MR 937477 (89e:34065)

Similar Articles

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

Retrieve articles in all journals with MSC: 34C10

Additional Information

Keywords: Oscillation theory, Forced differential equations
Article copyright: © Copyright 1993 American Mathematical Society

American Mathematical Society