Abstract and Applied Analysis

Nontrivial Periodic Solutions to Some Semilinear Sixth-Order Difference Equations

Yuhua Long

Abstract

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, ${Z}_{\mathrm{2}}$ index theory, and variational technique. Our results only make some assumptions on the period $T$, which are very easy to verify and rather relaxed.

Article information

Source
Abstr. Appl. Anal., Volume 2014 (2014), Article ID 359105, 8 pages.

Dates
First available in Project Euclid: 2 October 2014

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1412273237

Digital Object Identifier
doi:10.1155/2014/359105

Mathematical Reviews number (MathSciNet)
MR3182277

Zentralblatt MATH identifier
07022221

Citation

Long, Yuhua. Nontrivial Periodic Solutions to Some Semilinear Sixth-Order Difference Equations. Abstr. Appl. Anal. 2014 (2014), Article ID 359105, 8 pages. doi:10.1155/2014/359105. https://projecteuclid.org/euclid.aaa/1412273237

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