We study both existence and the exact number of positive solutions of the problem . All righ . Iturria ðPkÞ k ju0j u0 0 þ f ðuÞ 1⁄4 0 in ð0;1Þ; uð0Þ 1⁄4 uð1Þ 1⁄4 0; <: where k is a positive parameter, p > 1, the nonlinearity f is positive in (0,1), and f ð0Þ 1⁄4 f ð1Þ 1⁄4 0. Assuming that f satisfies the condition lims!1 f ðsÞ ð1 sÞ 1⁄4 x > 0 where h 2 ð0; p 1Þ, we study its behavior near zero,...

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The multiple shooting method has proved to be a very reliable and eecient method for the solution of multipoint boundary value problems such as those obtained from the necessary conditions for the solutions of constrained optimal control problems. If this technique is also to be used for guidance purposes, special features have to be implemented to reach a computing speed which enables real-tim...