Multiple Periodic Solutions for Odd Perturbations of the Discrete Relativistic Operator

Petru Jebelean and Călin Şerban
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Petru Jebelean: Department of Mathematics, West University of Timişoara, 4, Blvd. V. Pârvan, 300223 Timişoara, Romania
Călin Şerban: Department of Mathematics, West University of Timişoara, 4, Blvd. V. Pârvan, 300223 Timişoara, Romania

Mathematics, 2022, vol. 10, issue 9, 1-9

Abstract: We obtain the existence of multiple pairs of periodic solutions for difference equations of type − Δ ( Δ u ( n − 1 ) 1 − | Δ u ( n − 1 ) | 2 ) = λ g ( u ( n ) ) ( n ∈ Z ) , where g : R → R is a continuous odd function with anticoercive primitive, and λ > 0 is a real parameter. The approach is variational and relies on the critical point theory for convex, lower semicontinuous perturbations of C 1 -functionals.

Keywords: discrete relativistic operator; periodic solution; critical point; genus (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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