Glasnik Matematicki, Vol. 38, No.2 (2003), 273-284.

TRIPLE SOLUTIONS FOR THE ONE-DIMENSIONAL p-LAPLACIAN

Haishen Lu, Donal O'Regan and Ravi P. Agarwal

Institute of Applied Mathematics, Academy of Mathematics and System Sciences, Chinese Academy of Science, Beijing, 100080, China

Department of Mathematics, National University of Ireland, Galway, Ireland

Department of Mathematical Sciences, Florida Institute of Technology, Melbourne, FL 32901-6975, USA
e-mail: agarwal@fit.edu


Abstract.   We give conditions on f involving pairs of lower and upper solutions which lead to the existence of at least three solutions to the two point boundary value problem

(|u'|p -2 u') = q(t) f(t,u,u')   on (0,1), u(0) = u(1) = 0.

2000 Mathematics Subject Classification.   34B15.

Key words and phrases.   Lower and upper solutions, three solutions, p-Laplace equation, Nagumo condition.


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