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

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 too...

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Bibliographic Details
Published inProceedings of the Edinburgh Mathematical Society Vol. 47; no. 2; pp. 257 - 270
Main Authors Averna, Diego, Bonanno, Gabriele
Format Journal Article
LanguageEnglish
Published Cambridge, UK Cambridge University Press 01.06.2004
Subjects
Boundary value problems
critical points
one-dimensional $p$-Laplacian
three solutions
two-point boundary-value problem
one-dimensional $p$-Laplacian
three solutions
two-point boundary-value problem
critical points
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ISSN0013-0915
1464-3839
DOI10.1017/S0013091502000767

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Summary: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
Bibliography:ark:/67375/6GQ-2994KCB1-L
istex:6CCD700C0D67C9154F27212714FDD10B3D6CE067
ArticleID:00076
PII:S0013091502000767
SourceType-Scholarly Journals-1
ObjectType-Feature-1
content type line 14
ISSN:0013-0915
1464-3839
DOI:10.1017/S0013091502000767