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Research Article | Open Access

Elliptic equations in R2 involving supercritical exponential growth

Universidad Nacional Mayor de San Marcos, Lima, Perú
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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.

Keywords

Trudinger-Moser inequalitysupercritical exponential growthmountain pass theoremelliptic equationvariational method

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Electronic Research Archive
Volume 32 Issue 9,
September 2024
Pages 5341-5356
DOI: 10.3934/era.2024247

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Cite this article:
Leuyacc YRS. Elliptic equations in R2 involving supercritical exponential growth. Electronic Research Archive, 2024, 32(9): 5341-5356. https://doi.org/10.3934/era.2024247

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Received: 16 July 2024
Revised: 09 September 2024
Accepted: 10 September 2024
Published: 18 September 2024
©2024 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)