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Types and criteria of nonoscillatory solutions for some second order

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Abstract

In this paper we discuss the following NFDE

$$[r(t)[x(t) - cx(t - \tau )']' + \smallint _a^b p(t,\xi )x[g(t,\xi )]d\sigma (\xi ) = 0$$

where τ>0, 1>c≥0, 0≤g(t, ε)≤t,r(t)>0,p(t, ε)>0, and some sufficient and necessary conditions are given, under which there are three types of nonoscillatory solutions for the above equation.

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References

  1. Ruan Jiong, Asymptotic Behavior of Second Order Nonlinear Functional Differential Equations,Fudan Xuebao (Natural Science),22: 3 (1983), 255–264.

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  2. Ruan Jiong, Oscillation of Second-Order Differential Equations with Deviating Argument,Chin. Ann. of Math.,5 (A):1 (1984), 605–618.

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  3. Kusaro, T. and Onose, H., Nonlinear Oscillation of Second Order Differential Equations with Deviating Argument,J. of Math. Soc. Japan,29: 3 (1977), 541–559.

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Authors and Affiliations

  1. Fudan University, China

    Ruan Jiong

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  1. Ruan Jiong
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Ruan, J. Types and criteria of nonoscillatory solutions for some second order. Acta Mathematicae Applicatae Sinica 3, 97–110 (1987). https://doi.org/10.1007/BF02057584

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  • DOI: https://doi.org/10.1007/BF02057584

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