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Positive solutions of a second order singular ordinary differential equation

par Bonheure, Denis ;Gomes, José-Maria;Sanchez, Luís
Référence Nonlinear analysis, 61, 8, page (1383-1399)
Publication Publié, 2005

Article révisé par les pairs

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Résumé :

We study the existence of positive solutions for the second-order ordinary differential equationu″+ku′t=c(t)g(u)with the initial condition u′(0)=0 in bounded intervals [0,M] and in [0,+∞[. Here k>1, c(t) is bounded and the growth of g at infinity is controlled by a critical exponent. In our approach a shooting argument of Beresticky, Lions and Peletier is combined with variational methods. © 2005 Elsevier Ltd. All rights reserved.