Hostname: page-component-cd9895bd7-gxg78 Total loading time: 0 Render date: 2024-12-24T18:47:41.274Z Has data issue: false hasContentIssue false

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
Affiliation:
Dipartimento di Matematica ed Applicazioni, Facoltà di Ingegneria, Università di Palermo, Viale delle Scienze, 90128 Palermo, Italy ([email protected])
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 ([email protected])
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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

Type
Research Article
Copyright
Copyright © Edinburgh Mathematical Society 2004