# Three Solutions of an Nth Order Three-Point Focal Type Boundary Value Problem

## Department

Mathematics

## Document Type

Article

## Publication Date

11-15-2008

## Abstract

We consider the following differential equation u^{(n)} (t) = F (t, u (t)), t ∈ [0, 1], together with the three-point focal type boundary conditions u^{(j)} (0) = 0, 0 ≤ j ≤ n - 3,u^{(n - 2)} (p) = 0, u^{(n - 1)} (1) = 0, where frac(1, 2) < p < 1. By using two different fixed-point theorems, we offer criteria for the existence of three positive solutions of this problem. Examples are also included to illustrate the results obtained

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