| Full text | |
| Author(s): |
Ledesma, Cesar T.
;
Miyagaki, Olimpio H.
Total Authors: 2
|
| Document type: | Journal article |
| Source: | Milan Journal of Mathematics; v. 90, n. 2, p. 36-pg., 2022-07-06. |
| Abstract | |
This work concerns with the existence of positive solutions for the following class of fractional elliptic problems, { (-Delta)(s)u + u = (integral(Omega)vertical bar u(y)vertical bar(p)/vertical bar x-y vertical bar(N-alpha) dy) vertical bar u vertical bar(p-2)u, in Omega (0.1) u = 0, R-N\Omega where s is an element of (0, 1), N > 2s, alpha is an element of (0, N), Omega subset of R-N is an exterior domain with smooth boundary partial derivative Omega not equal phi and p is an element of (2, 2(s)*). The main feature from problem (0.1) is the lack of compactness due to the unboundedness of the domain and the lack of the uniqueness of solution of the limit problem. To overcome the loss these difficulties we use splitting lemma combined with careful investigation of limit profiles of ground states of limit problem. (AU) | |
| FAPESP's process: | 19/24901-3 - Critical nonlocal quasilinear problem: existence, multiplicity and properties of the solutions |
| Grantee: | Olimpio Hiroshi Miyagaki |
| Support Opportunities: | Regular Research Grants |