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.

On Two-Point Right Focal Eigenvalue Problems

Patricia J.Y. Wong

R.P. Agarwal

Abstract

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