On multiplicity of positive solutions for N-Laplacian with singular and critical nonlinearity

Abstract

In this note, we study the existence of multiple positive solutions towhere , , , , and is a smooth bounded domain in . Under suitable assumptions on and , we show that there exists such that admits two solutions for and no solution for .

Keywords:

• singular problem
• critical exponent problem

AMS Subject Classifications:

• 35J20
• 35J65

Acknowledgments

The authors thank to referee for their valuable comments.