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Zeitschrift für Analysis und ihre Anwendungen


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Volume 17, Issue 3, 1998, pp. 691–713
DOI: 10.4171/ZAA/845

Published online: 1998-09-30

On Two-Point Right Focal Eigenvalue Problems

Patricia J.Y. Wong[1] and R.P. Agarwal[2]

(1) Nanyang Technological University, Singapore, Singapore
(2) National University of Singapore, Singapore

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.

Keywords: Eigenvalues, positive solutions, boundary value problems

Wong Patricia, Agarwal R.P.: On Two-Point Right Focal Eigenvalue Problems. Z. Anal. Anwend. 17 (1998), 691-713. doi: 10.4171/ZAA/845