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} = λ F (t, y, y^{'}, \dots, y^{(p)} (n \geq 2, t \in (0, 1))

y^{(i)} (0) = 0 (0 \leq i \leq p -1)

y^{(i)} (1) = 0 (p \leq i \leq n -1)

where $λ > 0$ and $1 \leq p \leq n -1$ are fixed. The values of $λ$ are characterized so that the boundary value problem has a positive solution. We also establish explicit intervals of $λ$ . 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