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January/February 2020 Hénon elliptic equations in $\mathbb R^2$ with subcritical and critical exponential growth
Eudes Mendes Barboza, João Marcos do Ó
Differential Integral Equations 33(1/2): 1-42 (January/February 2020).

Abstract

We study the Dirichlet problem in the unit ball $B_1$ of $\mathbb R^2$ for the Hénon-type equation of the form \begin{equation*} \begin{cases} -\Delta u =\lambda u+|x|^{\alpha}f(u) & \mbox{in } B_1, \\ \quad \ \ u = 0 & \mbox{on } \partial B_1, \end{cases} \end{equation*} where $f(t)$ is a $C^1$-function in the critical growth range motivated by the celebrated Trudinger-Moser inequality. Under suitable hypotheses on constant $\lambda$ and $f(t)$, by variational methods, we study the solvability of this problem in appropriate Sobolev s paces.

Citation

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Eudes Mendes Barboza. João Marcos do Ó. "Hénon elliptic equations in $\mathbb R^2$ with subcritical and critical exponential growth." Differential Integral Equations 33 (1/2) 1 - 42, January/February 2020.

Information

Published: January/February 2020
First available in Project Euclid: 6 February 2020

zbMATH: 07177893
MathSciNet: MR4060433

Subjects:
Primary: 35J20, 35J25, 47J30

Rights: Copyright © 2020 Khayyam Publishing, Inc.

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Vol.33 • No. 1/2 • January/February 2020
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