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Proceedings of the American Mathematical Society

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



Maintenance of oscillations under the effect of a periodic forcing term

Author: Athanassios G. Kartsatos
Journal: Proc. Amer. Math. Soc. 33 (1972), 377-383
MSC: Primary 34C10
MathSciNet review: 0330622
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Abstract: A necessary and sufficient condition is given for the oscillation of all solutions of the differential equation

$\displaystyle {x^{(n)}} + P(t,x,x', \cdots ,{x^{(n - 1)}}) = Q(t)$

where $ {x_1}P(t,{x_1},{x_2}, \cdots ,{x_n}) > 0$ for every $ {x_1} \ne 0$, and Q is a continuous periodic function. This result answers a question recently raised by J. S. W. Wong. It is also shown that a well-known sufficient condition for the existence of at least one nonoscillatory solution of the unperturbed equation guarantees, for a large class of equations, the nonexistence of bounded oscillatory solutions.

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Keywords: Oscillation of solutions, nonoscillation of solutions, nonlinear differential equations
Article copyright: © Copyright 1972 American Mathematical Society