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A boundary blow-up for a class of quasilinear elliptic problems with a gradient term

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Abstract

By a perturbation method and constructing comparison functions, we show the exact asymptotic behavior of solutions near the boundary to quasilinear elliptic problem

$$\left\{\begin{array}{ll}\mbox{div}\left(|\nabla u|^{m-2}\nabla u\right)-|\nabla u(x)|^{q(m-1)}=b(x)g(u),\quad x\in \Omega,\\u>0,\quad x\in \Omega,\\u|_{\partial\Omega}=+\infty,\end{array}\right.$$

where Ω is a C 2 bounded domain with smooth boundary, m>1,q∈(1,m/(m−1)], g∈C[0,∞)∩C 1(0,∞), g(0)=0, g is increasing on [0,∞), and b is non-negative and non-trivial in Ω, which may be singular on the boundary.

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Authors and Affiliations

  1. Institute of Mathematics, School of Mathematics and Computer Science, Nanjing Normal University, Jiangsu, Nanjing, 210097, China

    Chunlian Liu & Zuodong Yang

  2. College of Zhongbei, Nanjing Normal University, Jiangsu, Nanjing, 210046, China

    Chunlian Liu & Zuodong Yang

Authors
  1. Chunlian Liu
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  2. Zuodong Yang
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Correspondence to Zuodong Yang.

Additional information

Project Supported by the National Natural Science Foundation of China (Grant No. 10871060). Project Supported by the Natural Science Foundation of the Jiangsu Higher Education Institutions of China (Grant No. 08KJB110005).

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Liu, C., Yang, Z. A boundary blow-up for a class of quasilinear elliptic problems with a gradient term. J. Appl. Math. Comput. 33, 23–34 (2010). https://doi.org/10.1007/s12190-009-0271-4

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  • DOI: https://doi.org/10.1007/s12190-009-0271-4

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