Oscillations in neutral equations with periodic coefficients

Authors:
G. Ladas, Ch. G. Philos and Y. G. Sficas

Journal:
Proc. Amer. Math. Soc. **113** (1991), 123-134

MSC:
Primary 34K15; Secondary 34C10

MathSciNet review:
1045596

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Abstract | References | Similar Articles | Additional Information

Abstract: We obtain a necessary and sufficient condition for the oscillation of all solutions of the neutral delay differential equation: (1)

**[1]**Q. Chuanxi and G. Ladas,*Oscillations of neutral differential equations with variable coefficients*, Appl. Anal.**32**(1989), no. 3-4, 215–228. MR**1030096**, 10.1080/00036818908839850**[2]**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**, 10.1016/0022-247X(86)90172-1**[3]**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****[4]**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**, 10.1016/0022-0396(88)90077-0**[5]**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**, 10.1016/0022-247X(87)90045-X**[6]**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****[7]**Gerasimos Ladas,*Sharp conditions for oscillations caused by delays*, Applicable Anal.**9**(1979), no. 2, 93–98. MR**539534**, 10.1080/00036817908839256**[8]**G. Ladas and Y. G. Sficas,*Oscillations of neutral delay differential equations*, Canad. Math. Bull.**29**(1986), no. 4, 438–445. MR**860851**, 10.4153/CMB-1986-069-2**[9]**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**, 10.2307/2323283**[10]**-,*Necessary and sufficient conditions for oscillations of higher order delay differential equations*, Trans. Amer. Math. Soc.**285**(1984), 81-90.**[11]**Ch. G. Philos,*On the existence of nonoscillatory solutions tending to zero at ∞ for differential equations with positive delays*, Arch. Math. (Basel)**36**(1981), no. 2, 168–178. MR**619435**, 10.1007/BF01223686**[12]**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**, 10.1016/0022-247X(87)90326-X

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DOI:
http://dx.doi.org/10.1090/S0002-9939-1991-1045596-9

Article copyright:
© Copyright 1991
American Mathematical Society