Existence of Non-oscillatory Solutions for a Higher-order Nonlinear Neutral Difference Equation
نویسندگان
چکیده
This article concerns the solvability of the higher-order nonlinear neutral delay difference equation ∆ “ akn . . .∆ ` a2n∆(a1n∆(xn + bnxn−d)) ́” + s X j=1 pjnfj(xn−rjn ) = qn, where n ≥ n0 ≥ 0, d, k, j, s are positive integers, fj : R → R and xfj(x) ≥ 0 for x 6= 0. Sufficient conditions for the existence of non-oscillatory solutions are established by using Krasnoselskii fixed point theorem. Five theorems are stated according to the range of the sequence {bn}.
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