Positive solutions and nonlinear eigenvalue problems for functional differential equations Original Research Article

Values of λ are determined for which there exist positive solutions of the nth-order functional differential equation, (−1)n−ku(n)(t) = λa(t)f(ut), 0 < t < 1, satisfying the initial condition, u(s) = φ(s), −r ≤ s ≤ 0, and satisfying the boundary conditions, u(i)(0) = 0, 0 ≤ i ≤ k − 1, and u(j)(1) = 0, 0 ≤ j ≤ n − k − 1, where a and f are nonnegative valued.