Abstract
In the present paper, we propose a method to deal with non-ordered lower and upper solutions in the case of ODE's with singular coefficients. As an application, we study the existence of positive solutions for a two-point boundary value problem on]0, 1[ associated to the equation u + a(t)g(u) = 0, where the function g : R+ --> R+ is continuous with superlinear growth at infinity and the weight a(t) changes sign as well as it may present some singularities at t = 0 or t = 1.
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