Eigenvalues of an nTH order difference equation with (n, p) type conditions

Abstract

We consider the (n, p) boundary value problem Δny + λF(k, y, Δy, ⋯ ,Δn-2y) = λG(k, y, Δy, ⋯ ,Δn-1y), n - 1 ≤ k ≤ N, Δiy(0) = 0, 0 ≤ i ≤ n - 2, ΔPy(N + n - p) = 0 where λ > 0, n ≥ 2 and 0 ≤ p ≤ n - 1 is fixed. The values of λ are characterized so that the boundary value problem has a positive solutio n. Examples are also included to dwell upon the importance of the results obtain ed.