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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
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