| Texto completo | |
| Autor(es): |
Barboza, Eudes M.
;
Maia, Braulio B. V.
;
Miyagaki, Olimpio H.
;
Pucci, Patrizia
Número total de Autores: 4
|
| Tipo de documento: | Artigo Científico |
| Fonte: | NODEA-NONLINEAR DIFFERENTIAL EQUATIONS AND APPLICATIONS; v. 32, n. 5, p. 36-pg., 2025-07-23. |
| Resumo | |
The main goal here is to classify the stable solutions, or more generally, the solutions that remain stable outside a compact set of , of the following k-coupled Hardy-Henon elliptic system -Delta u(i)=k Sigma(j=1)beta(ij)|x|(alpha)|u(j)|(q+1)|u(i)|(q-1)u(i) in R-N,i=1,...,k, where q >= 1,N>2,alpha>-2,k is a fixed positive integer, and B=[beta(ij)](k)(i,j=1) is a real symmetric copositive matrix. We consider the critical Joseph-Lundgren exponent , introduced in (3), for the nonautonomous case, which is larger than the Sobolev critical exponent for Hardy-Henon type equations, given in (2). Thus, by setting , we prove certain Liouville-type results for stable solutions and solutions with finite Morse index when 3 <= p<p(c) . To achieve this, we employ techniques such as integral estimates based on the stability condition, the application of a monotonicity formula and a Pohozaev identity, and analysis via a blow-down sequence. Moreover, when p >= pc , we show that the system admits nontrivial stable solutions. Then, we establish sharp results regarding the range of p, addressing both the autonomous and nonautonomous vectorial cases. (AU) | |
| Processo FAPESP: | 23/09656-8 - Um estudo sobre equações diferenciais parciais elípticas do tipo Choquard |
| Beneficiário: | Braulio Brendo Vasconcelos Maia |
| Modalidade de apoio: | Bolsas no Brasil - Pós-Doutorado |
| Processo FAPESP: | 22/16407-1 - TESEd: Temático em Equações e Sistemas de Equações diferenciais |
| Beneficiário: | Ederson Moreira dos Santos |
| Modalidade de apoio: | Auxílio à Pesquisa - Temático |