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Nonoscillation theorems for certain second order nonlinear differential equations

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Abstract.

Some necessary and sufficient conditions for nonoscillation are established for the second order nonlinear differential equation

\((r(t)\psi(x(t))\vert x^{\prime}(t)\vert^{p-1}x^{\prime}(t))^{\prime}+c(t)f(x(t))=0,\quad t\ge t_0,\)

where p > 0 is a constant. These results are extensions of the earlier results of Hille, Wintner, Opial, Yan for second order linear differential equations and include the recent results of Li and Yeh, Kusano and Yoshida, Yang and Lo for half-linear differential equations.

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Authors and Affiliations

  1. South China Normal University, Guangzhou, P.R. China

    Zhiting Xu

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  1. Zhiting Xu
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Authors’ address: School of Mathematical Sciences, South China Normal University, Guangzhou 510631, P.R. China

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Xu, Z. Nonoscillation theorems for certain second order nonlinear differential equations. Monatsh Math 156, 187–199 (2009). https://doi.org/10.1007/s00605-008-0555-z

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  • DOI: https://doi.org/10.1007/s00605-008-0555-z

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