@article{Leuyacc2023, 
author = {Yony Raúl Santaria Leuyacc},
title = {Supercritical Trudinger-Moser inequalities with logarithmic weights in dimension two},
year = {2023},
journal = {AIMS Mathematics},
volume = {8},
number = {8},
pages = {18354-18372},
keywords = {Trudinger-Moser inequality, supercritical exponential growth, logarithmic weight variational methods, Schrödinger equation},
url = {https://www.sciopen.com/article/10.3934/math.2023933},
doi = {10.3934/math.2023933},
abstract = {In this work, we are interested in studying the existence of nontrivial weak solutions to the following class of Schrödinger equations         {                            −                      d            i            v                    (          w          (          x          )          ∇          u          )                                    =                                    f          (          x          ,          u          )          ,                                    x          ∈                      B            1                    (          0          )          ,                                      u                                    =                                    0          ,                                    x          ∈          ∂                      B            1                    (          0          )          ,                        where    w  (  x  )  =      (    ln  ⁡  (  1      /        |    x      |    )            )              β       for some    β  ∈  [  0  ,  1  ), the nonlinearity    f  (  x  ,  s  ) behaves like        exp    (  (  1  +  h  (      |    x      |    )  )      |    s            |              2              /            (      1      −      β      )        ) and    h is a continuous radial function such that    h  (  r  ) tends to infinity as    r tends to    1. The proof involves variational methods and a new version of Trudinger-Moser inequality.}
}