Abstract
In this paper, we study the multiplicity of periodic solutions for the second order Hamiltonian systems \(\ddot{u}+\nabla F(t,u)=0\) with the boundary condition \(u(0)-u(T)=\dot{u}(0)-\dot{u}(T)=0\), where the potential F is either subquadratic k(t)-concave or subquadratic \(\mu (t)\)-convex. Based on the reduction method and a three-critical-point theorem due to Brezis and Nirenberg, we obtain the multiplicity results, which complement and sharply improve some related results in the literature.
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The work is supported by the National Natural Science Foundation of China (11971393) and the Science and Technology Research Program of Chongqing Municipal Education Commission (No. KJQN202200523).
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Ye, Y., Liu, S. Notes on Multiple Periodic Solutions for Second Order Hamiltonian Systems. Qual. Theory Dyn. Syst. 21, 141 (2022). https://doi.org/10.1007/s12346-022-00673-z
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DOI: https://doi.org/10.1007/s12346-022-00673-z