| Abstract: |
| In this paper, we consider the following discrete nonlinear problem which is subject to a periodic nonlinear forcing term:
$$
A u = \lambda u +p(u) + h +\mu \overline{\phi}
$$
where $A$ is an $n\times n $ matrix with real components, $p: \R^n\to \R^n$ is a periodic forcing term, $\overline{\phi }$ is an eigenvector of $A^T,$ the transpose of $A$, corresponding to the simple real eigenvalue $\lambda ,$ and $h\in \R^n$ is a vector orthogonal to $\overline{\phi} .$
Conditions on these terms will be provided such that this problem will have infinitely many distinct solutions when $\mu =0.$ The results here are motivated by some recent results for discrete systems and by results obtained for boundary value problems for semilinear elliptic problems at resonance. |
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