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International Journal of Mathematics and Mathematical Sciences
Volume 2012, Article ID 794040, 13 pages
http://dx.doi.org/10.1155/2012/794040
Research Article

Two-Point Boundary Value Problems for a Class of Second-Order Ordinary Differential Equations

1Department of Mathematical Sciences, University of Texas at El Paso, Bell Hall 316, El Paso, TX 79968-0514, USA
2Department of Mathematical Sciences, University of Texas at El Paso, Bell Hall 124, El Paso, TX 79968-0514, USA

Received 14 October 2011; Accepted 27 December 2011

Academic Editor: Martin Bohner

Copyright © 2012 Indranil SenGupta and Maria C. Mariani. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We study the general semilinear second-order ODE 𝑢 + 𝑔 ( 𝑡 , 𝑢 , 𝑢 ) = 0 under different two-point boundary conditions. Using the method of upper and lower solutions, we obtain an existence result. Moreover, under a growth condition on 𝑔 , we prove that the set of solutions of 𝑢 + 𝑔 ( 𝑡 , 𝑢 , 𝑢 ) = 0 is homeomorphic to the two-dimensional real space.