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THREE SOLUTIONS FOR A QUASILINEAR TWO-POINT BOUNDARY-VALUE PROBLEM INVOLVING THE ONE-DIMENSIONAL p-LAPLACIAN

Published online by Cambridge University Press:  01 July 2004

Diego Averna  and
Gabriele Bonanno
Diego Averna
Affiliation:
Dipartimento di Matematica ed Applicazioni, Facoltà di Ingegneria, Università di Palermo, Viale delle Scienze, 90128 Palermo, Italy (averna@unipa.it)
Gabriele Bonanno
Affiliation:
Dipartimento di Informatica, Matematica, Elettronica e Trasporti, Facoltà di Ingegneria, Università di Reggio Calabria, Via Graziella (Feo di Vito), 89100 Reggio Calabria, Italy (bonanno@ing.unirc.it)
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Abstract

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In this paper we prove the existence of at least three classical solutions for the problem

$$ \left\{ \begin{aligned} \amp-(|u'|^{p-2}u')'=\lambda f(t,u)h(u'), \\ \ampu(a)=u(b)=0, \end{aligned} \right. $$

when $\lambda$ lies in an explicitly determined open interval.

Our main tool is a very recent three-critical-points theorem stated in a paper by D. Averna and G. Bonanno (Topolog. Meth. Nonlin. Analysis22 (2003), 93–103).

AMS 2000 Mathematics subject classification: Primary 34B15

Keywords

critical pointsthree solutionstwo-point boundary-value problemone-dimensional $p$-Laplacian
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 47 , Issue 2 , June 2004 , pp. 257 - 270
Copyright
Copyright © Edinburgh Mathematical Society 2004