| Texto completo | |
| Autor(es): |
Zuo, Jiabin
;
An, Tianqing
;
Fiscella, Alessio
Número total de Autores: 3
|
| Tipo de documento: | Artigo Científico |
| Fonte: | MATHEMATICAL METHODS IN THE APPLIED SCIENCES; v. 44, n. 1, p. 15-pg., 2020-08-24. |
| Resumo | |
The paper deals with the following Kirchhoff-type problem integral M (integral integral(R2N) 1/p(x,y)vertical bar v(x)-v(y)vertical bar(p(x,y))/vertical bar x-y vertical bar(N+p(x,y)s(x,y))dxdy(-Delta)(p(.))(s(.))v(x)=mu g(x,v)+vertical bar v vertical bar(r(x)-2)v in Omega, v = 0 in R-N\Omega, where M models a Kirchhoff coefficient,(-Delta)(p(.))(s(.)) is a variable s(.)-order p(.)-fractional Laplace operator, with s(.):Double-struck capital R-2N -> (0,1)and p(.) : R-2N -> (1,infinity). Here,Omega subset of R-N is a bounded smooth domain with N > p(x,y)s(x,y) for any (x,y)is an element of(Omega) over bar x (Omega) over bar ,mu is a positive parameter,gis a continuous and subcritical function, while variable exponent r(x)could be close to the critical exponent p(s)*(x)=N (p) over bar (x)/(N-(s) over bar (x)(p) over bar (x)), given with (p) over bar (x)=p(x,x) and (s) over bar (x)=s(x,x)for x is an element of(Omega) over bar. We prove the existence and asymptotic behavior of at least one non-trivial solution. For this, we exploit a suitable tricky step analysis of the critical mountain pass level, combined with a Brezis and Lieb-type lemma for fractional Sobolev spaces with variable order and variable exponent. (AU) | |
| Processo FAPESP: | 19/02512-5 - Sistemas e equações diferenciais parciais |
| Beneficiário: | Marcelo da Silva Montenegro |
| Modalidade de apoio: | Auxílio à Pesquisa - Temático |
| Processo FAPESP: | 17/19752-3 - Problemas fracionários com falta de compacidade |
| Beneficiário: | Alessio Fiscella |
| Modalidade de apoio: | Auxílio à Pesquisa - Regular |