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Asymptotic properties for solutions of differential equations with singular p(t)-Laplacian

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Abstract

This paper deals with the nonoscillatory solutions of the nonlinear differential equation \(\left( a(t)|x{^\prime }|^{p(t)-2}x{^\prime }\right) {^\prime }+b(t)|x|^{\lambda -2}x=0\) involving “singular” p(t)-Laplacian. Sufficient conditions are given for the existence of extremal solutions, which do not exist in the conventional cases. In addition, we prove the coexistence of extremal solutions and weakly increasing solutions. Some examples are given to illustrate our results.

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Acknowledgements

The first author was supported by the Czech Science Foundation under grant 20-11846 S. The second author was supported by JSPS KAKENHI Grant Number JP22K13942. The authors thank to the anonymous reviewer for his/her valuable suggestions that helped to improve this paper.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, Masaryk University, Kotlářská 2, 61137, Brno, Czech Republic

    Zuzana Došlá

  2. Faculty of Liberal Arts, Sciences and Global Education, Osaka Metropolitan University, Gakuen-cho 1-1, Naka-ku, Sakai, Osaka, 599-8531, Japan

    Kōdai Fujimoto

Authors
  1. Zuzana Došlá
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  2. Kōdai Fujimoto
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Correspondence to Kōdai Fujimoto.

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Communicated by Adrian Constantin.

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Došlá, Z., Fujimoto, K. Asymptotic properties for solutions of differential equations with singular p(t)-Laplacian. Monatsh Math 201, 65–78 (2023). https://doi.org/10.1007/s00605-023-01835-0

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