Periodic solutions for a class of non-autonomous Hamiltonian systems with -Laplacian

Zhiyong Wang; Zhengya Qian

Mathematica Bohemica (2024)

  • Volume: 149, Issue: 2, page 185-208
  • ISSN: 0862-7959

Abstract

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We investigate the existence of infinitely many periodic solutions for the -Laplacian Hamiltonian systems. By virtue of several auxiliary functions, we obtain a series of new super- growth and asymptotic- 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 .

How to cite

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Wang, Zhiyong, and Qian, Zhengya. "Periodic solutions for a class of non-autonomous Hamiltonian systems with $p(t)$-Laplacian." Mathematica Bohemica 149.2 (2024): 185-208. <http://eudml.org/doc/299450>.

@article{Wang2024,
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 $p(t)\equiv p=2$.},
author = {Wang, Zhiyong, Qian, Zhengya},
journal = {Mathematica Bohemica},
keywords = {auxiliary functions; $p(t)$-Laplacian systems; periodic solution; (C) condition; generalized mountain pass theorem},
language = {eng},
number = {2},
pages = {185-208},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Periodic solutions for a class of non-autonomous Hamiltonian systems with $p(t)$-Laplacian},
url = {http://eudml.org/doc/299450},
volume = {149},
year = {2024},
}

TY - JOUR
AU - Wang, Zhiyong
AU - Qian, Zhengya
TI - Periodic solutions for a class of non-autonomous Hamiltonian systems with $p(t)$-Laplacian
JO - Mathematica Bohemica
PY - 2024
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 149
IS - 2
SP - 185
EP - 208
AB - 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 $p(t)\equiv p=2$.
LA - eng
KW - auxiliary functions; $p(t)$-Laplacian systems; periodic solution; (C) condition; generalized mountain pass theorem
UR - http://eudml.org/doc/299450
ER -

References

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