Abstract
We consider the semi-linear elliptic equation Δ u + f ( x , u ) + g ( | x | ) x · ∇ u = 0 , in some exterior region of R n , n ⩾ 3 . It is shown that if f depends radially on its first argument and is nonincreasing in its second, boundary conditions force the unique solution to be radial. Under different conditions, we prove the existence of a positive radial asymptotic solution to the same equation.
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