Differential and Integral Equations

Hénon elliptic equations in $\mathbb R^2$ with subcritical and critical exponential growth

Eudes Mendes Barboza and João Marcos do Ó

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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.

Article information

Source
Differential Integral Equations, Volume 33, Number 1/2 (2020), 1-42.

Dates
First available in Project Euclid: 6 February 2020

Permanent link to this document
https://projecteuclid.org/euclid.die/1580958028

Mathematical Reviews number (MathSciNet)
MR4060433

Zentralblatt MATH identifier
07177893

Subjects
Primary: 35J20: Variational methods for second-order elliptic equations 35J25: Boundary value problems for second-order elliptic equations 47J30: Variational methods [See also 58Exx]

Citation

do Ó, João Marcos; Barboza, Eudes Mendes. Hénon elliptic equations in $\mathbb R^2$ with subcritical and critical exponential growth. Differential Integral Equations 33 (2020), no. 1/2, 1--42. https://projecteuclid.org/euclid.die/1580958028


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