Abstract
The existence of positive solutions are established for the third-order functional difference equation Δ 3 u( n) + a( n) f( n, u( w( n))) = 0, 0 ≤ n ≤ T, satisfying u( n) = φ( n), n 1 ≤ n ≤ 1, and u( n) = ψ( n), T + 3 ≤ n ≤ n 2, with φ(0) = φ(1) = ψ( T + 3) = 0. The results in this paper generalize and substantially improve recent work by Agarwal and Henderson on boundary value problems related to third-order difference equations.
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