RT Journal Article
T1 Existence of solutions of nth-order nonlinear difference equations with general boundary conditions
A1 Cabada Fernández, Alberto
A1 Dimitrov, Nikolay
K1 Difference equation
K1 Multiplicity of solutions
K1 Green's function
K1 Positive solutions
K1 Parameter dependence
AB The aim of this paper is to prove the existence of one or multiple solutions of nonlinear difference equations coupled to a general set of boundary conditions. Before to do this, we construct a discrete operator whose fixed points coincide with the solutions of the problem we are looking for. Moreover, we introduce a strong positiveness condition on the related Green's function that allows us to construct suitable cones where to apply adequate fixed point theorems. Once we have the general existence result, we deduce, as a particular case, the existence of solutions of a second order difference equation with nonlocal perturbed Dirichlet conditions.
PB Springer
SN 0252-9602
YR 2020
FD 2020-01
LK https://hdl.handle.net/10347/37806
UL https://hdl.handle.net/10347/37806
LA eng
NO Cabada, A., Dimitrov, N. Existence of Solutions of nth-Order Nonlinear Difference Equations with General Boundary Conditions. Acta Math Sci 40, 226–236 (2020). https://doi.org/10.1007/s10473-020-0115-y
NO This version of the article has been accepted for publication, after peer review, and is subject to Springer Nature’s AM terms of use, but is not the Version of Record and does not reflect post-acceptance improvements, or any corrections. The Version of Record is available online at: https://doi.org/10.1007/s10473-020-0115-y
NO First author was partially supported by Xunta de Galicia (Spain), project EM2014/032 and AIE, Spain and FEDER, grant MTM2016-75140-P. The second author was supported by the Bulgarian National Science Fundation under Project DN 12/4 “Advanced Analytical and Numerical Methods for Nonlinear Differential Equations with Applications in Finance and Environmental Pollution”, 2017.
DS Minerva
RD 29 abr 2026