Existence of solutions for a class of fractional elliptic problems on exterior domains

被引:18
|
作者
Alves, Claudianor O. [1 ]
Bisci, Giovanni Molica [2 ]
Torres Ledesma, Cesar E. [3 ]
机构
[1] Univ Fed Campina Grande, Unidade Acad Matemat, BR-58429970 Campina Grande, Paraiba, Brazil
[2] Univ Urbino Carlo Bo, Dipartimento Sci Pure & Applicate DiSPeA, Piazza Repubbl 13, I-61029 Urbino, Italy
[3] Univ Nacl Trujillo, Dept Matemat, Av Juan Pablo II S-N, Trujillo, Peru
关键词
POSITIVE SOLUTION; SCHRODINGER-EQUATION; GROUND-STATES; LAPLACIAN;
D O I
10.1016/j.jde.2019.11.068
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
This work concerns with the existence of solutions for the following class of nonlocal elliptic problems {(-Delta)(s) u + u = vertical bar u vertical bar(p-2) u in Omega, u >= 0 in Omega and u not equivalent to 0, u = 0 R-N\ Omega, involving the fractional Laplacian operator (-Delta)(s) , where s is an element of (0, 1), N > 2s, Omega subset of R-N is an exterior domain with (non-empty) smooth boundary partial derivative Omega and p is an element of (2, 2(s)*). The main technical approach is based on variational and topological methods. The variational analysis that we perform in this paper dealing with exterior domains is quite general and may be suitable for other goals too. (C) 2019 Elsevier Inc. All rights reserved.
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页码:7183 / 7219
页数:37
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