For 1/2 < p < 1 fixed, values of lambda > 0 are determined for which there exist positive solutions of the n-th order differential equation u((n)) = lambda g(t)f(u), 0 < t < 1, satisfying the three-point boundary conditions, u((i-1)) (0) = u((n-2)) (P) = u((n-1)) (1) = 0, 1
The problem is converted to a third order differential-integro boundary value problem and then a recent result of Graef and Yang for third order boundary value problems is adapted. An example is included to illustrate the results.
Graef, J.R., Henderson, J., & Yang, B. (2006) Positive solutions of a nonlinear n-th order eigenvalue problem. Dynamics Of Continuous Discrete And Impulsive Systems - Series A -Mathematical Analysis, 13, 39-48.