Periodic solutions for a class of non-autonomous Hamiltonian systems with $p(t)$-Laplacian

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 mul...

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Bibliographic Details
Published inMathematica bohemica Vol. 149; no. 2; pp. 185 - 208
Main Authors Zhiyong Wang, Zhengya Qian
Format Journal Article
LanguageEnglish
Published Institute of Mathematics of the Czech Academy of Science 01.07.2024
Subjects
(c) condition
auxiliary functions
generalized mountain pass theorem
p(t)$-laplacian systems
periodic solution
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Summary: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 $p(t)\equiv p=2$.
ISSN:0862-7959
2464-7136
DOI:10.21136/MB.2023.0096-22