Electronic Journal of Differential Equations,
Vol. 2021 (2021), No. 20, pp. 1-18.

Title: Henon equation with nolinearities involving Sobolev critical growth in H^1
       
Authors: Eudes M. Barboza (Univ. Federal Rural de Pernambuco, PE, Brasil)
         Olimpio H. Miyagaki (Univ. Federal de Sao Carlos, SP, Brazil)
         Fabio R. Pereira (Univ. Federal de Juiz de Fora, MG, Brazil)
         Claudia R. Santana (Univ. Estadual de Santa Cruz, BA, Brazil)

Abstract:
 In this article we study the Hénon equation
 $$\displaylines{ 
 -\Delta u=\lambda |x|^{\mu} u+|x|^{\alpha}|u|^{ 2_{\alpha}^*-2}u\quad\text{in }B_1,\cr
 u =0\quad\text{on }\partial B_1,
 }$$
 where B<sub>1</sub> is the ball centered at the origin of R<sup>N</sup> (N&ge; 3) and
 &mu;&ge;&alpha;&ge;0. Under appropriate hypotheses on the constant &lambda;,
 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.