@article{Liu2024, 
author = {Chunlian Liu and Shuang Wang and Fanfan Chen},
title = {Resonance with Landesman-Lazer conditions for parameter-dependent equations: a multiplicity result via the Poincaré-Birkhoff theorem},
year = {2024},
journal = {AIMS Mathematics},
volume = {9},
number = {10},
pages = {28320-28340},
keywords = {periodic solutions, Poincaré-Birkhoff theorem, resonance, Landesman-Lazer conditions, parameter-dependent},
url = {https://www.sciopen.com/article/10.3934/math.20241374},
doi = {10.3934/math.20241374},
abstract = {We investigate the resonance problem and prove the existence of multiple periodic solutions to a second order parameter-dependent equation  x″+f(t,x)=sp(t). We weaken the usual requirement on the sublinearity of perturbations when  |x| becomes large; and develop a more general method to investigate the rotational characterizations of the Landesman-Lazer conditions. Furthermore,  f does not satisfy the common sign condition, and even the global existence of the solution is not guaranteed.}
}