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Boundary Behavior of Large Solutions to the Infinity Laplace Equations on the Half-Line

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Abstract

By adopting the method of upper and lower solutions, this article shows the blow-up rate of the unique nonnegative viscosity solution \(l(t)\) of the boundary value problem

$$(u'(t))^{2}u''(t) =b(t)f(u(t)), \quad u(t)>0, \quad t>0, \qquad u(0)=\infty, \quad u(\infty)=0,$$

where \(b\in C^{1}(0,\infty)\), which is positive and nondecreasing on \((0,\infty)\) (and may vanish at zero).

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Data sharing is not applicable to this article as no datasets were generated or analysed during the current study.

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Acknowledgments

The authors are greatly indebted to the anonymous referee for the very valuable suggestions and comments which surely improved the quality of the paper.

Funding

This work was supported by National Natural Science Foundation of China (grant no. 11771196) and Natural Science Foundation of Shandong Province (grant no. ZR2021MF090).

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Authors and Affiliations

  1. School of Mathematics and Statistics, Qilu University of Technology (Shandong Academy of Sciences), Jinan, Shandong, 250353, China

    Ling Mi

  2. Key Laboratory of Computing Power Network and Information Security, Ministry of Education, Shandong Computer Science Center, Qilu University of Technology (Shandong Academy of Sciences), Jinan, Shandong, 250353, China

    Chuan Chen

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  1. Ling Mi
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Correspondence to Ling Mi.

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Mi, L., Chen, C. Boundary Behavior of Large Solutions to the Infinity Laplace Equations on the Half-Line. Math Notes 114, 883–894 (2023). https://doi.org/10.1134/S0001434623110238

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