@article{Leuyacc2024, 
author = {Yony Raúl Santaria Leuyacc},
title = {Elliptic equations in  R2 involving supercritical exponential growth},
year = {2024},
journal = {Electronic Research Archive},
volume = {32},
number = {9},
pages = {5341-5356},
keywords = {Trudinger-Moser inequality, supercritical exponential growth, mountain pass theorem, elliptic equation, variational method},
url = {https://www.sciopen.com/article/10.3934/era.2024247},
doi = {10.3934/era.2024247},
abstract = {In this work, we investigated the existence of nontrivial weak solutions for the equation   −div(w(x)∇u)=f(x,u),x∈R2,where  w(x) is a positive radial weight, the nonlinearity  f(x,s) possesses growth at infinity of the type  exp((α0+h(|x|))|s|2/(1−β)), with  α0>0,  0<β<1 and  h is a continuous radial function that may be unbounded at infinity. To show the existence of weak solutions, we used variational methods and a new type of the Trudinger-Moser inequality defined on the whole two-dimensional space.}
}