@article{Leuyacc2023, 
author = {Yony Raúl Santaria Leuyacc},
title = {Hamiltonian elliptic system involving nonlinearities with supercritical exponential growth},
year = {2023},
journal = {AIMS Mathematics},
volume = {8},
number = {8},
pages = {19121-19141},
keywords = {Hamiltonian system, Trudinger-Moser inequality, supercritical exponential growth, variational methods, linking theorem},
url = {https://www.sciopen.com/article/10.3934/math.2023976},
doi = {10.3934/math.2023976},
abstract = {In this paper, we deal with the existence of nontrivial solutions to the following class of strongly coupled Hamiltonian systems:           {                            −                      d            i            v                                (                    w          (          x          )          ∇          u                      )                              =                    g          (          x          ,          v          )          ,                                                    x          ∈                      B            1                    (          0          )          ,                                      −                      d            i            v                                (                    w          (          x          )          ∇          v                      )                              =                    f          (          x          ,          u          )          ,                                                    x          ∈                      B            1                    (          0          )          ,                                      u          =          v          =          0                                                    x          ∈          ∂                      B            1                    (          0          )          ,                        where    w  (  x  )  =      (    log  ⁡  1      /        |    x      |              )              γ      ,    0  ≤  γ  <  1, and the nonlinearities    f and    g possess exponential growth ranges above the exponential critical hyperbola. Our approach is based on Trudinger-Moser type inequalities for weighted Sobolev spaces and variational methods.}
}