Abstract
In this paper, we study a discrete nonlinear boundary value problem that involves a nonlinear term oscillating near the origin and a power-type nonlinearity $$u^p$$ . By using variational methods, we establish the existence of a sequence of non-negative weak solutions that converges to 0 if $$p\ge 1$$ . In the sublinear case, we prove that for all n positive integer, the problem has at least n weak solutions if the parameter lies in a certain range.
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