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<p/> <p>First, existence criteria for at least three nonnegative solutions to the following boundary value problem of fourth-order difference equation &#916;⁴<it>x</it>(<it>t</it>-2) = <it>a</it>(<it>t</it>)<it>f</it>(<it>x</it>(<it>t</it>)),<it>t</it> &#8712; [2, <it>T</it>], <it>x</it>(0) = <it>x</it>(<it>T</it> + 2) = 0, &#916;²<it>x</it>(0) = &#916;²<it>x</it>(<it>T</it>) = 0 are established by using the well-known Leggett-Williams fixed point theorem, and then, for arbitrary positive integer <it>m</it>, existence results for at least 2<it>m</it>-1 nonnegative solutions are obtained.</p>