Abstract
A sufficient condition was obtained for oscillation of all solutions of theodd-order delay differential equation
wherep i (t) are non-negative real valued continuous function in [T ∞] for someT≥0 and σi,∈(0, ∞)(i = 1,2,…,m). In particular, forp i (t) =p i ∈(0, ∞) andn > 1 the result reduces to
implies that every solution of (*) oscillates. This result supplements forn > 1 to a similar result proved by Ladaset al [J. Diff. Equn.,42 (1982) 134–152] which was proved for the casen = 1.
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Das P, Oscillation of odd-order delay equations,Proc. Indian Acad. Sci. (Math. Sci.) 103 (1993) 341–347
Das P, Oscillation criteria for odd-order neutral equations,J. Math. Anal. Appl. 188 (1994) 245–257
Das P, Necessary and sufficient conditions for oscillation of neutral equations with periodic coefficients,Czech. Math. J. 44 (1994) 281–291
Das P, Oscillation of odd-order neutral equations,Czech. Math. J. (to appear)
Gopalsamy K, Lalli B S and Zhang B G, Oscillation of odd-order neutral differential equations,Czech. Math. J. 42 (1992) 313–323
Ladas G, Philos Ch G and Sficas Y G, Oscillation in neutral equations with periodic coefficients,Proc. Am. Math. Soc. 113 (1991) 123–133
Ladas G, Sficas Y G and Stavroulakis I P, Necessary and sufficient conditions for oscillations of higher order delay differential equations,Trans. Am. Math. Soc. 285 (1984) 81–90
Ladas G and Stavroulakis I P, Oscillations caused by several retarded and advanced arguments.J. Diff. Equn.,44 (1982) 134–152
Ladde G S, Lakshmikantham V and Zhang B G, Oscillation theory of differential equations with deviating arguments, (New York and Basel: Marcel Dekker) (1987)
Philos Ch G, Oscillations of some delay differential equations with periodic coefficients,J. Math. Anal. Appl. 162 (1992) 452–475
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Das, P., Misra, N. & Mishra, B.B. Oscillation of higher order delay differential equations. Proc. Indian Acad. Sci. (Math. Sci.) 105, 417–423 (1995). https://doi.org/10.1007/BF02836878
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DOI: https://doi.org/10.1007/BF02836878