Multiple positive solutions for a second-order boundary value problem on the half-line


In this paper we are concerned with the existence and localization of multiple positive solutions of a boundary value problem on the half-line associated to second-order differential equations. We use a variational approach based on critical point theory in conical shells and a Harnack type inequality. The specific compactness involved by the problems on infinite intervals is guaranteed by a growth condition on the nonlinear term which is tempered towards infinity.


Habiba Boulaiki
Faculty of Mathematics, USTHB, El-Alia Bab-ezzouar, Algiers, Algeria

Toufik Moussaoui
Laboratory of Fixed Point Theory and Applications, Ecole Normale Superieure, Kouba, Algiers, Algeria

Radu Precup
Department of Mathematics, Babes-Bolyai University, Cluj-Napoca, Romania


Critical point; Mountain-pass lemma; Compression; Positive solution; Harnack inequality

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H. Boulaiki, T. Moussaoui, R. Precup, Multiple positive solutions for a second-order boundary value problem on the half-line, J. Nonlinear Funct. Anal. 2017 (2017), Art. ID 17, 1-25,


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Journal Nonlinear Functional Analysis

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Mathematical Research Press

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