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

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

Juan C. Cardeno, Alfonso Castro

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.

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Juan C. Cardeño
Facultad de Ciencias Naturales y Matemáticas
Universidad de Ibagué
Ibagué, Tolima, Colombia
Alfonso Castro
Department of Mathematics
Harvey Mudd College
Claremont, CA 91711, USA

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