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

[摘要] In this paper we prove the existence of at least three classical solutions for the problem$$ left{ egin{aligned} amp-(|u'|^{p-2}u')'=lambda f(t,u)h(u'), \ ampu(a)=u(b)=0, end{aligned} ight. $$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

[学科分类] 数学（综合）

[关键词] critical points;three solutions;two-point boundary-value problem;one-dimensional $p$-Laplacian