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We consider the existence of multiple positive solutions of a nonlinear two-point boundary value problem by modifying a "time map" technique introduced by J. Smoller and A. Wasserman. We count the number of positive solutions and find their Conley indices and thus determine their stabilities. 1991 Mathematics subject classification (Amer. Math. Soc): 58 F 14, 34 B 15.doi:10.1017/s1446788700035060 fatcat:clasq75ndvduji3p25m4ng36ki