Oscillations in neutral equations with periodic coefficients
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- by G. Ladas, Ch. G. Philos and Y. G. Sficas PDF
- Proc. Amer. Math. Soc. 113 (1991), 123-134 Request permission
Abstract:
We obtain a necessary and sufficient condition for the oscillation of all solutions of the neutral delay differential equation: (1) \[ \tfrac {d}{{dt}}[x(t) + px(t - \tau )] + Q(t)x(t - \sigma ) = 0,\] where $p \in {\mathbf {R}},Q \in C[[0,\infty ),{{\mathbf {R}}^ + }],Q$ is $\omega$-periodic with $\omega > 0,Q(t)[unk]0$ for $t \geqq 0$, and there exist positive integers ${n_1}$ and ${n_2}$ such that $\tau = {n_1}\omega$ and $\sigma = {n_2}\omega$. More precisely we show that every solution of (1) oscillates if and only if every solution of an associated neutral equation with constant coefficients oscillates.References
- Q. Chuanxi and G. Ladas, Oscillations of neutral differential equations with variable coefficients, Appl. Anal. 32 (1989), no. 3-4, 215–228. MR 1030096, DOI 10.1080/00036818908839850
- M. K. Grammatikopoulos, E. A. Grove, and G. Ladas, Oscillations of first-order neutral delay differential equations, J. Math. Anal. Appl. 120 (1986), no. 2, 510–520. MR 864767, DOI 10.1016/0022-247X(86)90172-1
- M. K. Grammatikopoulos, G. Ladas, and Y. G. Sficas, Oscillation and asymptotic behavior of neutral equations with variable coefficients, Rad. Mat. 2 (1986), no. 2, 279–303 (English, with Serbo-Croatian summary). MR 873703
- M. K. Grammatikopoulos, Y. G. Sficas, and I. P. Stavroulakis, Necessary and sufficient conditions for oscillations of neutral equations with several coefficients, J. Differential Equations 76 (1988), no. 2, 294–311. MR 969427, DOI 10.1016/0022-0396(88)90077-0
- E. A. Grove, G. Ladas, and A. Meimaridou, A necessary and sufficient condition for the oscillation of neutral equations, J. Math. Anal. Appl. 126 (1987), no. 2, 341–354. MR 900752, DOI 10.1016/0022-247X(87)90045-X
- R. G. Koplatadze and T. A. Chanturiya, Oscillating and monotone solutions of first-order differential equations with deviating argument, Differentsial′nye Uravneniya 18 (1982), no. 8, 1463–1465, 1472 (Russian). MR 671174
- Gerasimos Ladas, Sharp conditions for oscillations caused by delays, Applicable Anal. 9 (1979), no. 2, 93–98. MR 539534, DOI 10.1080/00036817908839256
- G. Ladas and Y. G. Sficas, Oscillations of neutral delay differential equations, Canad. Math. Bull. 29 (1986), no. 4, 438–445. MR 860851, DOI 10.4153/CMB-1986-069-2
- G. Ladas, Y. G. Sficas, and I. P. Stavroulakis, Necessary and sufficient conditions for oscillations, Amer. Math. Monthly 90 (1983), no. 9, 637–640. MR 719755, DOI 10.2307/2323283 —, Necessary and sufficient conditions for oscillations of higher order delay differential equations, Trans. Amer. Math. Soc. 285 (1984), 81-90.
- Ch. G. Philos, On the existence of nonoscillatory solutions tending to zero at $\infty$ for differential equations with positive delays, Arch. Math. (Basel) 36 (1981), no. 2, 168–178. MR 619435, DOI 10.1007/BF01223686
- Y. G. Sficas and I. P. Stavroulakis, Necessary and sufficient conditions for oscillations of neutral differential equations, J. Math. Anal. Appl. 123 (1987), no. 2, 494–507. MR 883704, DOI 10.1016/0022-247X(87)90326-X
Additional Information
- © Copyright 1991 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 113 (1991), 123-134
- MSC: Primary 34K15; Secondary 34C10
- DOI: https://doi.org/10.1090/S0002-9939-1991-1045596-9
- MathSciNet review: 1045596