Table of Contents
International Journal of Analysis
Volume 2014, Article ID 638976, 18 pages
http://dx.doi.org/10.1155/2014/638976
Research Article

Solvability of a Third-Order Singular Generalized Left Focal Problem in Banach Spaces

Department of Mathematics, Hexi University, Gansu 734000, China

Received 9 February 2014; Accepted 5 May 2014; Published 26 May 2014

Academic Editor: Chuanxi Qian

Copyright © 2014 Youwei Zhang. 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 consider the existence of positive solution for a third-order singular generalized left focal boundary value problem with full derivatives in Banach spaces. Green’s function and its properties, explicit a priori, estimates will be presented. By means of the theories of the fixed point in cones, we establish some new and general results on the existence of single and multiple positive solutions to the third-order singular generalized left focal boundary value problem. Our results are generalizations and extensions of the results of the focal boundary value problem. An example is included to illustrate the results obtained.