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International Journal of Differential Equations
Volume 2016, Article ID 1683759, 18 pages
Research Article

A New Result Concerning the Solvability of a Class of General Systems of Variational Equations with Nonmonotone Operators: Applications to Dirichlet and Neumann Nonlinear Problems

1Department of Mathematics and Applications “R. Caccioppoli”, University of Naples “Federico II”, Via Cintia, Monte S. Angelo, I-80126 Naples, Italy
2University of Naples, Via Roma 29, 81031 Aversa, Italy

Received 30 July 2015; Accepted 28 September 2015

Academic Editor: Jianshe Yu

Copyright © 2016 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.


A new result of solvability for a wide class of systems of variational equations depending on parameters and governed by nonmonotone operators is found in a Banach real and reflexive space with applications to Dirichlet and Neumann problems related to nonlinear elliptic systems.