On positive entire solutions to a class of equations with a singular coefficient and critical exponent (Q1907688)

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.