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Asymptotic behavior of oscillatory solutions of a differential equation with deviating arguments. (English) Zbl 0472.34044


MSC:

34K25 Asymptotic theory of functional-differential equations
34E05 Asymptotic expansions of solutions to ordinary differential equations
34C10 Oscillation theory, zeros, disconjugacy and comparison theory for ordinary differential equations
34K99 Functional-differential equations (including equations with delayed, advanced or state-dependent argument)
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References:

[1] Bihari, I., A generalization of a lemma of Bellman and its application to uniqueness problems of differential equations, Acta Math. Acad. Sci. Hungar., 7, 81-94 (1956) · Zbl 0070.08201
[2] Kusano, T.; Onose, H., Asymptotic decay of oscillatory solutions of second order differential equations with forcing term, (Proc. Amer. Math. Soc., 66 (1977)), 251-257 · Zbl 0367.34021
[3] Singh, B., Asymptotically vanishing oscillatory trajectories in second order retarded equations, SIAM J. Math. Anal., 7, 37-44 (1976) · Zbl 0321.34058
[4] Singh, B., A correction to “Forced oscillations in general ordinary differential equations with deviating arguments,”, Hiroshima Math. J., 9, 297-302 (1979) · Zbl 0409.34070
[6] Singh, B., Necessary and sufficient conditions for eventually vanishing oscillatory solutions of functional equations with small delays, Internat. J. Math. Math. Sci., 1, 269-283 (1978) · Zbl 0389.34048
[8] Staikos, V. A.; Philos, Ch. G., Nonoscillatory phenomena and damped oscillations, Nonlinear Anal., 2, 197-210 (1978) · Zbl 0378.34057
[9] Trench, W. F., Canonical forms and principal systems in general disconjugate equations, Trans. Amer. Math. Soc., 189, 319-327 (1974) · Zbl 0289.34051
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