J Austral Math Soc Ser B 39 pp386--407, 1998.

Eigenvalue characterization for (n, p) boundary-value problems

Patricia J. Y. Wong and Ravi P. Agarwal

(Received 24 January 1996; revised 10 May 1996)

Abstract

We consider the (n, p) boundary value problem

y⁽ⁿ⁾ + lH(t, y) = lK(t, y), n ³ 2, t Î (0, 1),
y^(p)(1) = y⁽ⁱ⁾(0) = 0, 0 £ i £ n - 2,

where l > 0 and 0 £ p £ n - 1 is fixed. We characterize the values of l such that the boundary value problem has a positive solution. For the special case l = 1, we also offer sufficient conditions for the existence of positive solutions of the boundary value problem.

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Authors

Patricia J. Y. Wong: Division of Mathematics, Nanyang Technological University, 469 Bokit Timah Road, Singapore 259756
Ravi P. Agarwal: Department of Mathematics, National University of Singapore, 10 Kent Ridge Crescent, Singapore 119260

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Last Modified: Mon Dec 17 17:08:26 2001