Variational and Topological Methods: Theory, Applications, 
Numerical Simulations, and Open Problems.
Electron. J. Diff. Eqns., Conference 21 (2014), pp. pp. 23-30.

Title: Existence of positive solutions for a superlinear elliptic system with
       Neumann boundary condition

Authors: Juan C. Cardeno (Univ. de Ibague, Tolima, Colombia)
         Alfonso Castro  (Harvey Mudd College, Claremont, CA, USA)
 
Abstract: 
 We prove the existence of a positive solution for a class of nonlinear
 elliptic systems with Neumann boundary conditions. The proof combines
 extensive use of a priori estimates for elliptic problems with Neumann
 boundary condition and Krasnoselskii's compression-expansion theorem.

Published February 10, 2014.
Math Subject Classifications: 35J20, 35J60, 35B38.
Key Words: Semilinear elliptic system; a priori estimates; ordered Banach space;
           contraction-expansion operator; Neumann boundary condition.