On Two-Point Right Focal Eigenvalue Problems

Patricia J.Y. Wong; R.P. Agarwal

doi:10.4171/zaa/845

JournalszaaVol. 17, No. 3pp. 691–713

On Two-Point Right Focal Eigenvalue Problems

Patricia J.Y. Wong
Nanyang Technological University, Singapore, Singapore
R.P. Agarwal
National University of Singapore, Singapore

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Abstract

We consider the boundary value problem

(–1)^{n–p}y^{(n} = \lambda F(t, y, y', \dots, y^{(p)} \ \ \ (n ≥ 2, t \in (0,1))

y^{(i)} (0) = 0 \ \ \ (0 ≤ i ≤ p–1)

y^{(i)} (1) = 0 \ \ \ (p ≤ i ≤ n–1)

where $\lambda > 0$ and $1 ≤ p ≤ n–1$ are fixed. The values of $\lambda$ are characterized so that the boundary value problem has a positive solution. We also establish explicit intervals of $\lambda$ . Examples are included to dwell upon the importance of the results obtained.

Cite this article

Patricia J.Y. Wong, R.P. Agarwal, On Two-Point Right Focal Eigenvalue Problems. Z. Anal. Anwend. 17 (1998), no. 3, pp. 691–713

DOI 10.4171/ZAA/845