Abstract and Applied Analysis
Volume 2012 (2012), Article ID 154307, 18 pages
http://dx.doi.org/10.1155/2012/154307
Research Article

Study on the Existence and Uniqueness of Solution of Generalized Capillarity Problem

Li Wei,1 Liling Duan,1 and Haiyun Zhou2

1School of Mathematics and Statistics, Hebei University of Economics and Business, Shijiazhuang 050061, China
2Institute of Applied Mathematics and Mechanics, Ordnance Engineering College, Shijiazhuang 050003, China

Received 6 September 2012; Accepted 22 November 2012

Academic Editor: Jiaxin Hu

Copyright © 2012 Li Wei et al. 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

By using the perturbation theories on sums of ranges of nonlinear accretive mappings of Calvert and Gupta (1978), the abstract result on the existence and uniqueness of the solution in of the generalized Capillarity equation with nonlinear Neumann boundary value conditions, where and denotes the dimension of , is studied. The equation discussed in this paper and the methods here are a continuation of and a complement to the previous corresponding results. To obtain the results, some new techniques are used in this paper.