Multiple periodic solutions of a class of second-order partial difference equations via Morse theory

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Abstract

Based on Morse theory and the mountain pass lemma, we investigate the existence and multiplicity of nontrivial periodic solutions for a class of second-order partial difference equations. If the nonlinearity is resonant or sublinear at infinity, a series of results under reasonable assumptions are established. Also, two examples are provided to illustrate our main results. Our obtained results generalize and improve some existing ones.

Keywords

partial difference equation / nontrivial periodic solution / Morse theory / mountain pass lemma / resonance / sublinear

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