Uniqueness of non-negative solutions of a class of semi-linear elliptic equations

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This article is concerned with boundary value problems of the type (BVP) u″ + g(r)u′ + f(u) = 0, r > 0; u′(0) = 0, limr → ∞ u(r) = 0; where f(0) = 0. Such problems arise in the study of semi-linear elliptic differential equations in ℝn. It is shown that (BVP) has at most one non-negative non-trivial solution under appropriate conditions on f and g. The conditions are weaker than those given by Peletier and Serrin [6], who considered the special case g(r) = (n - 1)/r, n = 2, 3,⋯.