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Abstract and Applied Analysis
Volume 2012, Article ID 760854, 44 pages
Research Article

Dirichlet and Neumann Problems Related to Nonlinear Elliptic Systems: Solvability, Multiple Solutions, Solutions with Positive Components

Department of Mathematics and Applications, “R. Caccioppoli.,” University of Naples “Federico II”, Via Claudio 21, 80125 Naples, Italy

Received 1 February 2012; Accepted 2 April 2012

Academic Editor: D. O'Regan

Copyright © 2012 Luisa Toscano and Speranza Toscano. 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 study the solvability of Dirichlet and Neumann problems for different classes of nonlinear elliptic systems depending on parameters and with nonmonotone operators, using existence theorems related to a general system of variational equations in a reflexive Banach space. We also point out some regularity properties and the sign of the found solutions components. We often prove the existence of at least two different solutions with positive components.