Departamento de Matemática
Universidade de Brasília - UnB
70910-900, Brasília - DF, Brazil
email: giovany@unb.br
Departamento de Matemática
Universidade de Brasília - UnB
70910-900, Brasí\lia - DF, Brazil
email: georgekiametis@gmail.com
Giovany M. Figueiredo, George Kiametis
Abstract:
In this article we use a Palais-Smale sequence satisfying a
property related to Pohozaev identity to show the existence of
solution for the elliptic Caffarelli-Kohn-Nirenberg type problems
$$
-\text{div}(|x|^{-ap}|\nabla u|^{p-2}\nabla u)
+ |x|^{-bp^{*}}|u|^{p-2}u= |x|^{-bp^{*}}h(u) \quad \text{in }\mathbb{R}^N
$$
and
$$
-\text{div}(|x|^{-ap}|\nabla u|^{p-2}\nabla u)
= |x|^{-bp^{*}} f(u) \quad \text{in }\mathbb{R}^N,
$$
where \(1< p< N\), \(0\leq a< \frac{N-p}{p^{*}}\), \(a< b\leq a+1\),
\( p^{*}=p^{*}(a,b)=\frac{pN}{N-dp}\) and \(d=1+a-b\). and \(h\) and
\(f\) are continuous functions that satisfy hypotheses considered by
Berestycki and Lions in [7].
Submitted January 15, 2024. Published August 12, 2024.
Math Subject Classifications: 35B38, 35J35, 35J92.
Key Words: Caffarelli-Kohn-Nirenberg type problems; Nehari manifold.
DOI: 10.58997/ejde.2024.44
Show me the PDF file (373 KB), TEX file for this article.
|
Giovany M. Figueiredo Departamento de Matemática Universidade de Brasília - UnB 70910-900, Brasília - DF, Brazil email: giovany@unb.br |
|---|---|
|
George D. F. L. Kiametis Departamento de Matemática Universidade de Brasília - UnB 70910-900, Brasí\lia - DF, Brazil email: georgekiametis@gmail.com |
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