Positive solutions of superlinear boundary value problems with singular indefinite weight

M. Gaudenzi; P. Habets; F. Zanolin

doi:10.3934/cpaa.2003.2.411

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2003, Volume 2, Issue 3: 411-423. Doi: 10.3934/cpaa.2003.2.411

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Positive solutions of superlinear boundary value problems with singular indefinite weight

1.
Dipartimento di Finanzia dell'Impresa e dei Mercati Finanziari, Università, Via Tomadini 30, I-33100 Udine
2.
Institut de Mathématiques Pures et Appliquées, Chemin du Cyclotron 2, B-1348 Louvain-la-Neuve
3.
Dipartimento di Matematica e Informatica, Università, Via Delle Scienze 206, I-33100 Udine

Received: July 2002

Revised: March 2003

Published: September 2003

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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 $g: \quad \mathbb R^+\to \mathbb R^+$ 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 $t= 1.$

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Mathematics Subject Classification: 34B15, 34L40.

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