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
On Two-Point Right Focal Eigenvalue Problems cover
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Abstract

We consider the boundary value problem

(1)npy(n=λF(t,y,y,,y(p)   (n2,t(0,1))(–1)^{n–p}y^{(n} = \lambda F(t, y, y', \dots, y^{(p)} \ \ \ (n ≥ 2, t \in (0,1))
y(i)(0)=0   (0ip1)y^{(i)} (0) = 0 \ \ \ (0 ≤ i ≤ p–1)
y(i)(1)=0   (pin1)y^{(i)} (1) = 0 \ \ \ (p ≤ i ≤ n–1)

where λ>0\lambda > 0 and 1pn11 ≤ p ≤ n–1 are fixed. The values of λ\lambda are characterized so that the boundary value problem has a positive solution. We also establish explicit intervals of λ\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