The authors consider the higher order boundary-value problem u (n)(t) = q(t)f(u(t)), 0 ≤ t ≤ 1, u(i-1)(0) = u (n-2)(p) = u(n-1)(1) = 0, 1 ≤ i ≤ n -2, where n ≥ 4 is an integer, and p ∈ (1/2, 1) is a constant. Sufficient conditions for the existence and nonexistence of positive solutions of this problem are obtained. The main results are illustrated with an example.
Electronic Journal of Differential Equations
Graef, J.R., Henderson, J., & Yang, B. (2007) Positive solutions of a nonlinear higher order boundary-value problem. Electronic Journal of Differential Equations, 2007, 1-10.