Quasilinear elliptic equation involving singular non-linearities

Abstract

We consider the existence of solutions for the quasilinear elliptic equation

under Dirichlet boundary conditions, where Ω⊂R ^N is a bounded domain with smooth boundary. The most important fact here is that either g or f (or both of them) is singular at 0 if g(t), . By means of a direct variational approach, we establish the existence of a solution with -norms.

Keywords:

• quasilinear elliptic equation
• singular
• existence
• uniqueness
• large solutions

2000 AMS Subject Classifications: :

• 35J60
• 35J65
• 35K60

Acknowledgements

The authors are supported by the Natural Science Foundation of the Jiangsu Higher Education Institutions of China (Grant No. 08KJB).