Electron. J. Differential Equations, Vol. 2021 (2021), No. 20, pp. 1-18.

Henon equation with nolinearities involving Sobolev critical growth in H1

Eudes M. Barboza, Olimpio H. Miyagaki, Fabio R. Pereira, Claudia R. Santana

In this article we study the Hénon equation

where B1 is the ball centered at the origin of RN (N≥ 3) and μ≥α≥0. Under appropriate hypotheses on the constant λ, we prove existence of at least one radial solution using variational methods.

Submitted October 2, 2019. Published March 29, 2021.
Math Subject Classifications: 35J20, 35J25, 35B33, 35B34.
Key Words: Henon type equation; critical Sobolev growth; resonance; noncompact variational problem.

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Eudes M. Barboza
Departamento de Matemática
Universidade Federal Rural de Pernambuco
50740-560, Recife - PE, Brasil
email: eudes.barboza@ufrpe.br
Olimpio H. Miyagaki
Department of Mathematics
Universidade Federal de São Carlos
13565-905, São Carlos - SP, Brazil
email: olimpio@ufscar.br, ohmiyagaki@gmail.com
Fábio R. Pereira
Departamento de Matemática
Universidade Federal de Juiz de Fora
36036-330 - Juiz de Fora - MG, Brazil
email: fabio.pereira@ufjf.edu.br
Cláudia R. Santana
Departamento de Ciências Exatas e Tecnológicas
Universidade Estadual de Santa Cruz
45662-900 Ilhéeus - BA, Brazil
email: santana@uesc.br

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