Existence of solutions for some higher order boundary value problems - Charkrit S. (2014)
In this paper, we are concerned with the existence of solutions for the higher order boundary value problem in the formu(2 m + 2) (x) = f (x, u (x), u″ (x), ..., u(2 m) (x)), x ∈ (0, 1),u(2 i) (0) = u(2 i) (1) = 0, 0 ≤ i ≤ m, where m is a given positive integer and f : [0, 1] × Rm + 1 → R is continuous. We introduce a new maximum principle of higher order equations and develop a monotone method in the presence of lower and upper solutions for this problem. © 2006 Elsevier Inc. All rights reserved.