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This paper deals with semilinear elliptic equations in an exterior domain of R N with N ≥ 3. Sufficient conditions are obtained for the equation to have a positive solution which decays at infinity. The main result is proved by means of a supersolution-subsolution method presented by Noussair and Swanson. By using phase plane analysis of a system of Liénard type, a suitable positive supersolution is found out. Asymptotic decay estimation on a solution of the Liénard system gains a positivedoi:10.1090/s0002-9939-02-06681-9 fatcat:csylox4jxzeljfnabyxnvj5aki