数学物理学报(英文版) ›› 2005, Vol. 25 ›› Issue (2): 283-295.

• 论文 • 上一篇    下一篇

LOCATION OF THE BLOW UP POINT FOR POSITIVE SOLUTIONS OF A BIHARMONIC EQUATION INVOLVING NEARLY CRITICAL EXPONENT

耿堤   

  1. Department of Mathematics, South China Normal University, Guangzhou 510631, China
  • 出版日期:2005-04-20 发布日期:2005-04-20
  • 基金资助:

    The research work was supported by the National Natural Foundation of China
    (10371045) and Guangdong Provincial Natural Science Foundation of China (000671).

LOCATION OF THE BLOW UP POINT FOR POSITIVE SOLUTIONS OF A BIHARMONIC EQUATION INVOLVING NEARLY CRITICAL EXPONENT

 GENG Di   

  • Online:2005-04-20 Published:2005-04-20
  • Supported by:

    The research work was supported by the National Natural Foundation of China
    (10371045) and Guangdong Provincial Natural Science Foundation of China (000671).

摘要:

In this paper a semilinear biharmonic problem involving nearly critical growth
with Navier boundary condition is considered on an any bounded smooth domain. It is
proved that positive solutions concentrate on a point in the domain, which is also a critical
point of the Robin’s function corresponding to the Green’s function of biharmonic operator
with the same boundary condition. Similar conclusion has been obtained in [6] under the
condition that the domain is strictly convex

Abstract:

In this paper a semilinear biharmonic problem involving nearly critical growth
with Navier boundary condition is considered on an any bounded smooth domain. It is
proved that positive solutions concentrate on a point in the domain, which is also a critical
point of the Robin’s function corresponding to the Green’s function of biharmonic operator
with the same boundary condition. Similar conclusion has been obtained in [6] under the
condition that the domain is strictly convex

Key words: Biharmonic operator;Navier boundary conditions, asymptotic behavior;
critical exponents,
Green’s function

中图分类号: 

  • 35B50