Existence of solutions for the p-Laplacian with critical Sobolev exponent and convection

Abstract

In this article, we study the existence of solutions for the p-Laplacian involving critical Sobolev exponent and convection based on the theory of the Leray–Schauder degree for non-compact mappings.

Keywords:

• critical Sobolev exponent
• p-Laplacian equation
• convection

AMS Subject Classifications:

• 35A01
• 35J92

Acknowledgements

This work was partially supported by the National Science Foundation of China, and by a Specific Foundation for Ph.D Specialities of Educational Department of China.