Geodesic
Periodic solutions for a class of non-autonomous Hamiltonian systems with $p(t)$-Laplacian
Mathematica Bohemica, Tome 149 (2024) no. 2, pp. 185-208
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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 $p(t)\equiv p=2$.
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 $p(t)\equiv p=2$.
DOI : 10.21136/MB.2023.0096-22
Classification : 34C25, 35A15
Keywords: auxiliary functions; $p(t)$-Laplacian systems; periodic solution; (C) condition; generalized mountain pass theorem 
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Wang, Zhiyong; Qian, Zhengya. Periodic solutions for a class of non-autonomous Hamiltonian systems with $p(t)$-Laplacian. Mathematica Bohemica, Tome 149 (2024) no. 2, pp. 185-208. doi: 10.21136/MB.2023.0096-22

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