Nontrivial periodic solutions to some semilinear sixth-order difference equations. (English) Zbl 1473.39021

Summary: We establish some new criteria to guarantee nonexistence, existence, and multiplicity of nontrivial periodic solutions of some semilinear sixth-order difference equations by using minmax method, \(Z_2\) index theory, and variational technique. Our results only make some assumptions on the period \(T\), which are very easy to verify and rather relaxed.


39A23 Periodic solutions of difference equations
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