Existence of bounded positive solutions of quasi-linear elliptic equations

Abstract

Existence of bounded positive solutions of a class of quasi-linear elliptic equation is obtained in exterior domain of R ^N , N ≥ 1. Firstly, by using fixed point theory, the existence theorem of a class of ordinary differential equation is established. Then, by constructing super-solution and sub-solution, the existence of bounded positive solutions of quasi-linear elliptic equation is given. The results of this article are new and extend previously known results.

Keywords:

• existence
• quasi-linear elliptic equation
• super-solution
• sub-solution

AMS Subject Classifications::

• 35J65
• 35B25

Acknowledgements

This project is supported by the National Natural Science Foundation of China (Grant No. 10871060) and the Natural Science Foundation of the Jiangsu Higher Education Institutions of China (Grant No. 08KJB110005).