数学物理学报(英文版)

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THE EXISTENCE AND GLOBAL OPTIMAL ASYMPTOTIC BEHAVIOUR OF LARGE SOLUTIONS FOR A SEMILINEAR ELLIPTIC PROBLEM

张志军   

  1. 烟台大学数学与信息学院, 烟台 264005
  • 收稿日期:2005-11-17 修回日期:2006-12-25 出版日期:2008-07-20 发布日期:2008-07-20
  • 通讯作者: 张志军
  • 基金资助:

    This work is supported by the National Natural Science Foundation of China (10671169)

THE EXISTENCE AND GLOBAL OPTIMAL ASYMPTOTIC BEHAVIOUR OF LARGE SOLUTIONS FOR A SEMILINEAR ELLIPTIC PROBLEM

Zhang Zhijiun   

  1. School of Mathematics and Informational Science, Yantai University, Yantai 264005, China
  • Received:2005-11-17 Revised:2006-12-25 Online:2008-07-20 Published:2008-07-20
  • Contact: Zhang Zhijiun

摘要:

By Karamata regular variation theory and constructing comparison functions, the author shows the existence and global optimal asymptotic behaviour of solutions for a semilinear elliptic problem △u=k(x)g(u), u>0, x in Omega,
u|_{\partial \Omega}=+∞, where Omega is a bounded domain with smooth boundary in RN; g ∈ C1[0,∞), g(0)=g'(0)=0, and there exists p>1, such that $\lim\limits_{s\rightarrow \infty}\frac {g(s \xi)}{g(s)}=\xi^p$, $\forall \ \xi>0$, and $k \in C_{\rm loc}^\alpha(\Omega)$ is non-negative non-trivial in Omega which may be singular on the boundary.

关键词: Semilinear elliptic equations, explosive subsolutions, explosive supersolutions, existence, the global optimal asymptotic behaviour

Abstract:

By Karamata regular variation theory and constructing comparison functions, the author shows the existence and global optimal asymptotic behaviour of solutions for a semilinear elliptic problem △u=k(x)g(u), u>0, x in Omega,
u|_{\partial \Omega}=+∞, where Omega is a bounded domain with smooth boundary in RN; g ∈ C1[0,∞), g(0)=g'(0)=0, and there exists p>1, such that $\lim\limits_{s\rightarrow \infty}\frac {g(s \xi)}{g(s)}=\xi^p$, $\forall \ \xi>0$, and $k \in C_{\rm loc}^\alpha(\Omega)$ is non-negative non-trivial in Omega which may be singular on the boundary.

Key words: Semilinear elliptic equations, explosive subsolutions, explosive supersolutions, existence, the global optimal asymptotic behaviour

中图分类号: 

  • 35J60