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Proceedings of the Edinburgh Mathematical Society (1)

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THREE SOLUTIONS FOR A QUASILINEAR TWO-POINT BOUNDARY-VALUE PROBLEM INVOLVING THE ONE-DIMENSIONAL p-LAPLACIAN
Diego Averna, Gabriele Bonanno
Journal:

Proceedings of the Edinburgh Mathematical Society / Volume 47 / Issue 2 / June 2004

Published online by Cambridge University Press:

01 July 2004, pp. 257-270
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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