Electronic Journal of Differential Equations,
Vol. 2012 (2012), No. 192, pp. 1-13.

Title: Existence and multiplicity of solutions for nonlinear discrete inclusions
 
Authors: Nicu Marcu (Univ. of Craiova, Romania)
         Giovanni Molica Bisci (Univ. of Reggio Calabria, Italy)

Abstract:
 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 04, 2012. Published November 02, 2012.
Math Subject Classifications: 38J20, 39A10, 34B15, 49J40
Key Words: Nonlinear algebraic systems; difference equations;
 non-smooth problems; variational methods