# On Two-Point Right Focal Eigenvalue Problems

### Patricia J.Y. Wong

Nanyang Technological University, Singapore, Singapore### R.P. Agarwal

National University of Singapore, Singapore

## 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