Periodic solutions for a class of non-autonomous Hamiltonian systems with $p(t)$-Laplacian
Zhiyong Wang, Zhengya Qian
Received June 3, 2022. Published online March 28, 2023.
Abstract: We investigate the existence of infinitely many periodic solutions for the $p(t)$-Laplacian Hamiltonian systems. By virtue of several auxiliary functions, we obtain a series of new super-$p^+$ growth and asymptotic-$p^+$ growth conditions. Using the minimax methods in critical point theory, some multiplicity theorems are established, which unify and generalize some known results in the literature. Meanwhile, we also present an example to illustrate our main results are new even in the case $p(t)\equiv p=2$.
Affiliations: Zhiyong Wang (corresponding author), Zhengya Qian, Department of Mathematics, Nanjing University of Information Science & Technology, Nanjing 210044, Jiangsu, P. R. China, e-mail: firstname.lastname@example.org, email@example.com