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September  2003, 2(3): 411-423. doi: 10.3934/cpaa.2003.2.411

Positive solutions of superlinear boundary value problems with singular indefinite weight

M. Gaudenzi 1, , P. Habets 2, and  F. Zanolin 3,

1. 

Dipartimento di Finanzia dell'Impresa e dei Mercati Finanziari, Università, Via Tomadini 30, I-33100 Udine, Italy
2. 

Institut de Mathématiques Pures et Appliquées, Chemin du Cyclotron 2, B-1348 Louvain-la-Neuve, Belgium
3. 

Dipartimento di Matematica e Informatica, Università, Via Delle Scienze 206, I-33100 Udine, Italy

Received  July 2002 Revised  March 2003 Published  June 2003

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 $t= 1.$
Keywords: singular coe±cients., Positive solutions, indefinite weight, superlinear equations.
Mathematics Subject Classification: 34B15, 34L4.
Citation: M. Gaudenzi, P. Habets, F. Zanolin. Positive solutions of superlinear boundary value problems with singular indefinite weight. Communications on Pure & Applied Analysis, 2003, 2 (3) : 411-423. doi: 10.3934/cpaa.2003.2.411
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