Monotone Methods Applied to Some Higher Order Bound- Ary Value Problems
نویسندگان
چکیده
We prove the existence of a solution for the nonlinear boundary value problem u = f ( x, u, u′′, . . . , u ) , x ∈ [0, 1], u(0) = 0 = u(1), 0 ≤ i ≤ m + 1, where f : [0, 1] × R → R is continuous. The technique used here is a monotone method in the presence of upper and lower solutions. We introduce a new maximum principle which generalizes one due to Bai which in turn was an improvement of a maximum principle by Ma.
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