Tang, Xianhua; Zhang, Xingyong Periodic solutions for second-order Hamiltonian systems with a \(p\)-Laplacian. (English) Zbl 1219.34057 Ann. Univ. Mariae Curie-Skłodowska, Sect. A 64, No. 1, 93-113 (2010). The authors considered two second-order Hamiltonian systems with a \(p\)-Laplacian. Using the improved Sobolev inequality and Wirtinger’s inequality, and the least action principle, they obtain some existence conditions for periodic solutions of these two systems. Reviewer: Fengqin Zhang (Yuncheng) Cited in 5 Documents MSC: 34C25 Periodic solutions to ordinary differential equations 70H05 Hamilton’s equations 58E50 Applications of variational problems in infinite-dimensional spaces to the sciences 37J45 Periodic, homoclinic and heteroclinic orbits; variational methods, degree-theoretic methods (MSC2010) Keywords:second-order Hamiltonian systems; \(p\)-Laplacian; periodic solution; Sobolev’s inequality; Wirtinger’s inequality; least action principle PDFBibTeX XMLCite \textit{X. Tang} and \textit{X. Zhang}, Ann. Univ. Mariae Curie-Skłodowska, Sect. A 64, No. 1, 93--113 (2010; Zbl 1219.34057) Full Text: DOI