Multiple critical orbits to partial periodic perturbations of the p-relativistic operator. (June 2020)

• Record Type: Journal Article
• Authors: Jebelean, Petru; Mawhin, Jean; Şerban, Călin
• Is Part Of: Applied mathematics letters. Volume 104(2020)
• Publication Date: 2020-06
• Subjects: Relativistic operator -- Periodic solutions -- Periodic nonlinearities -- Critical orbits; Applied mathematics -- Periodicals; 519.05
• DOI: 10.1016/j.aml.2020.106220
• Languages: English
• ISSNs: 0893-9659

Abstract

Abstract: We prove the existence of m + 1 geometrically distinct periodic solutions for N -dimensional systems involving the p -relativistic operator R p u ≔ | u ′ | p − 2 u ′ ( 1 − | u ′ | p ) 1 − 1 ∕ p ′ and an m -periodic potential; here m < N . This is obtained by reduction to an equivalent non-singular problem for which the existence of multiple critical orbits can be inferred.