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Journal of Applied Mathematics
Volume 2014, Article ID 705298, 7 pages
Research Article

Method of Lower and Upper Solutions for Elliptic Systems with Nonlinear Boundary Condition and Its Applications

Department of Mathematics, Northwest Normal University, Lanzhou 730070, China

Received 8 March 2014; Accepted 30 April 2014; Published 12 May 2014

Academic Editor: Wan-Tong Li

Copyright © 2014 Ruyun Ma 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.


We develop the method of lower and upper solutions for a class of elliptic systems with nonlinear boundary conditions. As its application, an elliptic system modeling a population divided into juvenile and adult age groups is studied, and we find sufficient conditions in terms of the principal eigenvalue of the corresponding linearized system, to guarantee the existence of coexistence states of the above juvenile-adult model.