A note on positive evanescent solutions for a certain class of elliptic problems

This paper is devoted to the existence and properties of solutions of the following class of nonlinear elliptic differential equations Δ u ( x ) + f ( x , u ( x ) ) + g ( ‖ x ‖ ) x ⋅ ∇ u ( x ) = 0 , x ∈ R n , ‖ x ‖ > R . We prove existence of positive solutions vanishing at positive infinity. Our approach is based on the subsolution and supersolution method. The nonlinearity f covers both sublinear and superlinear cases and does not necessarily satisfy f ( x , 0 ) ≡ 0 . The asymptotic behavior of solutions is also described.