@article{Liu2022, 
author = {Chunlian Liu},
title = {Non-resonance with one-sided superlinear growth for indefinite planar systems via rotation numbers},
year = {2022},
journal = {AIMS Mathematics},
volume = {7},
number = {8},
pages = {14163-14186},
keywords = {periodic solutions, non-resonance, rotation numbers, one-sided superlinear, Poincaré-Bohl theorem},
url = {https://www.sciopen.com/article/10.3934/math.2022781},
doi = {10.3934/math.2022781},
abstract = {We consider the non-resonance with one-sided superlinear growth conditions for the indefinite planar system        z    ′    =  f  (  t  ,  z  ) from a rotation number viewpoint, and obtain the existence of    2  π-periodic solutions by applying a rotation number approach together with the Poincaré-Bohl theorem. We allow that the angular velocity of solutions of        z    ′    =  f  (  t  ,  z  ) is controlled by the angular velocity of solutions of two positively homogeneous and oddly symmetric systems        z    ′    =      L    i    (  t  ,  z  )  ,  i  =  1  ,  2 on the left half-plane, which have rotation numbers that satisfy    ρ  (      L    1    )  >  n      /    2 and    ρ  (      L    2    )  <  (  n  +  1  )      /    2, and allow    f  (  t  ,  z  ) to grow superlinearly on the right half-plane. In order to estimate the rotation angle difference of solutions, we develop a system methodology of "tracking" the angle difference of solutions of the system        z    ′    =  f  (  t  ,  z  ) on each small interval on the given side under sign-varying conditions.}
}