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2003, Volume 2, Issue 3: 411-423. Doi: 10.3934/cpaa.2003.2.411
This issue Previous Article On the Lyapunov functions for the solutions of the generalized Burgers equation Next Article

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:  June 30, 2002
Revised:  February 28, 2003
Published:  August 2003
Abstract Related Papers Cited by
    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 $t= 1.$
    Mathematics Subject Classification: 34B15, 34L40.

    Citation:
    shu

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