Abstract
Based on a continuation theorem of Mawhin, the existence of a periodic solution for a higher-order nonlinear neutral difference equation is studied. Our conclusion is new and interesting.
Highlights
The periodic solution theory of differential equation and difference equation has important academic value and application background
We study the periodic solutions of a higher-order nonlinear neutral difference equation of the form k[un + cun–σ ] = gn(un–τ1, un–τ2, . . . , un–τl ), n ∈ Z, (1)
We use a continuity theorem to give some criteria for the existence of a periodic solution of (1), and our conclusion is new and interesting
Summary
The periodic solution theory of differential equation and difference equation has important academic value and application background. As far as we know, the results of the periodic solutions of neutral difference equations are relatively few (see [7, 8]). We study the periodic solutions of a higher-order nonlinear neutral difference equation of the form k[un + cun–σ ] = gn(un–τ1 , un–τ2 , .
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