RT Journal Article
T1 Dirichlet systems with discrete relativistic operator
A1 Cabada Fernández, Alberto
A1 Jebelean, Petru
A1 Şerban, Călin
K1 Difference Equations
K1 Discrete relativistic operator
K1 Variational Methods
AB We 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.
PB Wiley
SN 0024-6093
YR 2023
FD 2023-12-26
LK https://hdl.handle.net/10347/39892
UL https://hdl.handle.net/10347/39892
LA eng
NO Cabada, A., Jebelean, P. and Şerban, C. (2024), Dirichlet systems with discrete relativistic operator. Bull. London Math. Soc., 56: 1149-1168
NO This 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.12986
NO The first author was supported by Grant PID2020-113275GB-I00 funded by MCIN/AEI/10.13039/501100011033 and by “ERDF A way of making Europe” of the “European Union”.
DS Minerva
RD 28 abr 2026