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Asymptotic Behavior of Unbounded Solutions of Second-Order Differential Equations with General Nonlinearities

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Abstract

One considers second-order ordinary differential equations with general nonlinearities and a bounded potential. Depending on the type of nonlinearity, qualitative behavior of solutions is described. For solutions that are unbounded near the boundaries of their domain, asymptotic formulas are obtained in the case of equations with constant or variable potentials.

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Authors and Affiliations

  1. Moscow State University, Moscow, Russia

    T. A. Korchemkina

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  1. T. A. Korchemkina
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Correspondence to T. A. Korchemkina.

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Translated from Trudy Seminara imeni I. G. Petrovskogo, No. 32, pp. 239–256, 2019.

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Korchemkina, T.A. Asymptotic Behavior of Unbounded Solutions of Second-Order Differential Equations with General Nonlinearities. J Math Sci 244, 267–277 (2020). https://doi.org/10.1007/s10958-019-04618-x

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  • DOI: https://doi.org/10.1007/s10958-019-04618-x

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