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Positive solutions of superlinear boundary value problems with singular indefinite weight

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  • 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 $g: \quad \mathbb R^+\to \mathbb R^+$ 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 $t= 1.$
    Mathematics Subject Classification: 34B15, 34L40.


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