Cabada Fernández, AlbertoJebelean, PetruŞerban, Călin2025-02-252025-02-252023-12-26Cabada, A., Jebelean, P. and Şerban, C. (2024), Dirichlet systems with discrete relativistic operator. Bull. London Math. Soc., 56: 1149-11680024-6093https://hdl.handle.net/10347/39892This is the Author Accepted Manuscript version of the following article: Cabada, A., Jebelean, P. and Şerban, C. (2024), Dirichlet systems with discrete relativistic operator. Bull. London Math. Soc., 56: 1149-1168, which has been published in final form at https://doi.org/10.1112/blms.12986We are concerned with Dirichlet systems involving the relativistic discrete operator $$ u \mapsto \Delta \left [ \frac{\Delta u(n-1)}{\sqrt{1 - |\Delta u(n-1)|^2}} \right ] \qquad \left (n \in \{1, \ldots, T\} \right ).$$ Here, for $u:\{0, \ldots, T+1\}\to \mathbb{R}^N,$ we denote $\Delta u(n-1):=u(n)-u(n-1)$. Besides an "universal" existence result for a system with a general nonlinearity, we obtain multiplicity of solutions for systems with parameterized nonlinearities. Our approaches mainly rely on Brouwer degree arguments and critical point theory for convex, lower semicontinuous perturbations of $C^1$-functionals.engAttribution-NonCommercial-NoDerivatives 4.0 Internationalhttp://creativecommons.org/licenses/by-nc-nd/4.0/Difference EquationsDiscrete relativistic operatorVariational Methods120207 Ecuaciones en diferenciasjournal article10.1112/blms.129861469-2120open access