Electron. J. Diff. Equ., Vol. 2012 (2012), No. 192, pp. 1-13.

Existence and multiplicity of solutions for nonlinear discrete inclusions

Nicu Marcu, Giovanni Molica Bisci

A non-smooth abstract result is used for proving the existence of at least one nontrivial solution of an algebraic discrete inclusion. Successively, a multiplicity theorem for the same class of discrete problems is also established by using a locally Lipschitz continuous version of the famous Brezis-Nirenberg theoretical result in presence of splitting. Some applications to tridiagonal, fourth-order and partial difference inclusions are pointed out.

Submitted September 4, 2012. Published November 2, 2012.
Math Subject Classifications: 38J20, 39A10, 34B15, 49J40
Key Words: Nonlinear algebraic systems; difference equations; non-smooth problems; variational methods

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Nicu Marcu
Department of Finance, University of Craiova
Street A.I. Cuza No. 13, 200585, Craiova, Romania
email: marcu.nicu@yahoo.com
Giovanni Molica Bisci
Dipartimento MECMAT, University of Reggio Calabria
Via Graziella, Feo di Vito, 89124 Reggio Calabria, Italy
email: gmolica@unirc.it

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