Title

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

Authors

John R. Graef, University of Tennessee - Chattanooga
Johnny Henderson, Baylor University
Patricia J. Y. Wong, Nanyang Technological University, Singapore
Bo Yang, Kennesaw State UniversityFollow

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