Positive radial symmetric solutions for a class of elliptic problems with critical exponent and -1 growth

Abstract

In this paper, we consider a class of semilinear elliptic equation with critical exponent and -1 growth. By using the critical point theory for nonsmooth functionals, two positive solutions are obtained. Moreover, the symmetry and monotonicity properties of the solutions are proved by the moving plane method. Our results improve the corresponding results in the literature.

Keywords

• singular elliptic equation
• critical growth
• radial symmetry
• critical point theory for nonsmooth functionals
• moving plane method
• 35b33
• 35j61
• 35j75