Eigenvalue characterization for a class of boundary value problems

[[abstract]]We consider the nth order ordinary differential equation (−1)n−ky (n) = λa(t)f(y), t ∈ [0, 1], n ≥ 3 together with boundary condition y (i) (0) = 0, 0 ≤ i ≤ k − 1, and y (l) (1) = 0, j ≤ l ≤ j +n−k −1, for 1 ≤ j ≤ k −1 fixed. Values of λ are characterized so that the boundary value problem has a positive solution.[[notice]]補正完