@article{Leuyacc2023, 
author = {Yony Raúl Santaria Leuyacc},
title = {Standing waves for quasilinear Schrödinger equations involving double exponential growth},
year = {2023},
journal = {AIMS Mathematics},
volume = {8},
number = {1},
pages = {1682-1695},
keywords = {quasilinear Schrödinger equation, double exponential growth, mountain pass theorem, Trudinger-Moser inequality, dual approach},
url = {https://www.sciopen.com/article/10.3934/math.2023086},
doi = {10.3934/math.2023086},
abstract = {We will focus on the existence of nontrivial, nonnegative solutions to the following quasilinear Schrödinger equation         {                            −                      d            i            v                                (                    log          ⁡                                    e                                                |                                x                                  |                                                              ∇          u                      )                    −                      d            i            v                                (                    log          ⁡                                    e                                                |                                x                                  |                                                              ∇          (                      u            2                    )                      )                    u                                    =                                    g          (          x          ,          u          )          ,                                    x          ∈                      B            1                    ,                                      u                                    =                                    0          ,                                    x          ∈          ∂                      B            1                    ,                        where        B    1   denotes the unit ball centered at the origin in              R        2   and    g behaves like        e    x    p    (      e                  s        4              ) as    s tends to infinity, the growth of the nonlinearity is motivated by a Trudinder-Moser inequality version, which admits double exponential growth. The proof involves a change of variable (a dual approach) combined with the mountain pass theorem.}
}