Abstract
This paper studies the positive solutions of the nonlinear second-order periodic boundary value problem $$u''\left( t \right) + \lambda \left( t \right)u\left( t \right) = f\left( {t,u\left( t \right)} \right), a.e. t \in \left[ {0,2\pi } \right], u\left( 0 \right) = u\left( {2\pi } \right),u'\left( 0 \right) = u'\left( {2\pi } \right),$$ where f(t, u) is a local Caratheodory function. This shows that the problem is singular with respect to both the time variable t and space variable u. By applying the Leggett-Williams and Krasnosel’skii fixed point theorems on cones, an existence theorem of triple positive solutions is established. In order to use these theorems, the exact a priori estimations for the bound of solution are given, and some proper height functions are introduced by the estimations.
Published Version
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