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In this paper we discuss the uniqueness of positive solutions of the nonlinear second order system -u'' = g(v), -v'' = f(u) in (-R,R), u(±R) = v(±R) = 0 where f and g satisfy some appropriate conditions. Our result applies, in particular, to g(v) = v, f(u) = up, p > 1, or f(u) = ?u + a1up1 + ... + akupk, with pj > 1, aj > 0 for j = 1, ..., k and 0 = ? < µ12 where µ1 = p2/4R2.

Uniqueness of positive solutions of nonlinear second order systems