On two-point right focal eigenvalue problems

Abstract

We consider the boundary value problem (-1)n - p y(n) = λF(t, y, y ,..., y(p)) (n ≥ 2, t ∈ (0, 1)) y(i) (0) = 0 (0 ≤ i ≤ p - 1) y(i) (1) = 0 (p ≤ i ≤ n - 1) where λ > 0 and 1 ≤ p ≤ 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. © Heldermann Verlag.