# zbMATH — the first resource for mathematics

On positive entire solutions to a class of equations with a singular coefficient and critical exponent. (English) Zbl 0847.35045
The author proves results on existence, uniqueness, and qualitative behavior of positive solutions to equations of the type $- \Delta u= a(x/ |x|) u|x|^{- 2}+ f(x, u)\quad \text{in} \quad \mathbb{R}^n\backslash \{0\}$ in relation with the behavior of the function $$a$$. The main results concern the critical nonlinearity $$f(s)= s^{(n+ 2)/(n- 2)}$$. The proofs use variational arguments and the moving plane method.
Reviewer: M.Biroli (Monza)

##### MSC:
 35J60 Nonlinear elliptic equations 35B40 Asymptotic behavior of solutions to PDEs 35J20 Variational methods for second-order elliptic equations