Abstract
In this paper, we provide sufficient conditions for the boundedness and unboundedness of the entire solutions for a semilinear elliptic system of the following type Δ u = p 1 | x | f u , v , x ∈ R N , Δ v = p 2 | x | g u , x ∈ R N , N ≥ 3 . Here p 1 , f , p 2 and g are continuous functions satisfying certain properties. Furthermore, we study the case where the system is not of a variational type. Our results are obtained by a straightforward application of the Arzela–Ascoli theorem.
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