| Full text | |
| Author(s): |
Zuo, Jiabin
;
Fiscella, Alessio
;
Bahrouni, Anouar
Total Authors: 3
|
| Document type: | Journal article |
| Source: | Complex Variables and Elliptic Equations; v. 67, n. 2, p. 17-pg., 2020-10-28. |
| Abstract | |
This paper is concerned with the existence and multiplicity of solutions for the fractional variable order Choquard type problem (-Delta)(p(center dot))(s(center dot))u(x) + (-Delta)(q(center dot))(s(center dot))u(x) = lambda vertical bar u(x)vertical bar beta(x)(-2)u(x) + (integral F-Omega(y, u(y))/|x - y vertical bar(mu(x,y)) dy)f (x, u(x)) + k(x) in Omega, u(x) = 0 in R-N\Omega, where (-Delta)(p(center dot))(s(center dot)) and (-Delta)(q(center dot))(s(center dot)) are two fractional Laplace operators with variable order s(center dot) : R-2N -> (0, 1) and with different variable exponents p(center dot) : R-2N -> (1, infinity) and q(center dot) : R-2N -> (1,infinity). Here Omega subset of R-N is a bounded smooth domain with at least N >= 2, lambda is a real parameter, beta, mu and k are continuous variable parameters, while F is the primitive function of a suitable f. Under some appropriate conditions on beta and k, through variational methods, we prove existence and multiplicity of solutions for the above problem. (AU) | |
| FAPESP's process: | 19/02512-5 - Systems and partial differential equations |
| Grantee: | Marcelo da Silva Montenegro |
| Support Opportunities: | Research Projects - Thematic Grants |
| FAPESP's process: | 19/23917-3 - Operator with non standard growth |
| Grantee: | Alessio Fiscella |
| Support Opportunities: | Regular Research Grants |