On oscillations of unbounded solutions
HTML articles powered by AMS MathViewer
- by I. Győri, G. Ladas and L. Pakula PDF
- Proc. Amer. Math. Soc. 106 (1989), 785-792 Request permission
Abstract:
Consider the differential equation with deviating arguments (1) \[ \dot y(t) + p[y(t - {\sigma _1}) - y(t - {\sigma _2})] = 0\] where $p,{\sigma _1}$ and ${\sigma _2}$ are real numbers. We prove that every unbounded solution of (1) oscillates if and only if the characteristic equation (2) \[ \lambda + p({e^{ - \lambda {\sigma _1}}} - {e^{ - \lambda {\sigma _2}}}) = 0\] has no positive roots and 0 is a simple root of (2).References
- Richard Bellman and Kenneth L. Cooke, Differential-difference equations, Academic Press, New York-London, 1963. MR 0147745
- C. Corduneanu, Almost periodic functions, Interscience Tracts in Pure and Applied Mathematics, No. 22, Interscience Publishers [John Wiley & Sons], New York-London-Sydney, 1968. With the collaboration of N. Gheorghiu and V. Barbu; Translated from the Romanian by Gitta Bernstein and Eugene Tomer. MR 0481915
- Walter Rudin, Real and complex analysis, McGraw-Hill Book Co., New York-Toronto, Ont.-London, 1966. MR 0210528 D. V. Widder, An introduction to transform theory, Academic Press, New York, 1971.
Additional Information
- © Copyright 1989 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 106 (1989), 785-792
- MSC: Primary 34K15; Secondary 44A10
- DOI: https://doi.org/10.1090/S0002-9939-1989-0969316-X
- MathSciNet review: 969316