Asymptotic forms of solutions of half-linear ordinary differential equations with integrable perturbations

Sokea Luey; Hiroyuki Usami

doi:10.32917/h2022005

July 2023 Asymptotic forms of solutions of half-linear ordinary differential equations with integrable perturbations

Sokea Luey, Hiroyuki Usami

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Hiroshima Math. J. 53(2): 171-189 (July 2023). DOI: 10.32917/h2022005

Abstract

We consider perturbed half-linear ordinary differential equations near $\infty$ . We clarify asymptotic forms of the nontrivial solutions as $t \to \infty$ under $p$ -th power integrability conditions imposed on the perturbations. Generalized Riccati equations associated with the half-linear equations under consideration are employed to prove the main results.

Funding Statement

This work was supported by JSPS KAKENHI Grant number 21K03307.

Acknowledgement

This work was supported by the Research Institute for Mathematical Sciences, an International Joint Usage/Research Center located in Kyoto University. The authors also would like to thank the referee for giving them appropriate comments.

Citation

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Sokea Luey. Hiroyuki Usami. "Asymptotic forms of solutions of half-linear ordinary differential equations with integrable perturbations." Hiroshima Math. J. 53 (2) 171 - 189, July 2023. https://doi.org/10.32917/h2022005