Fast and slow decay solutions for supercritical fractional elliptic problems in exterior domains

Ao Weiwei; Liu Chao; Wang Liping

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Fast and slow decay solutions for supercritical fractional elliptic problems in exterior domains

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We consider the fractional elliptic problem: { (-Delta)(s) u - u(P) = 0, u > 0 in R-N(B-1) over bar, u = 0 in (B-1) over bar, lim(vertical bar x vertical bar -> infinity) u(x) = 0 where B-1 is the unit ball in R-N, N >= 3, s is an element of (0, 1) and p > (N + 2s)/(N - 2s). We prove that this problem has infinitely many solutions with slow decay O(vertical bar x vertical bar(-2s/(P-1))) at infinity. In addition, for each s is an element of (0, 1) there exists P-s > (N + 2s)/(N - 2s), for any (N + 2s)/(N - 2s) < p < P-s, the above problem has a solution with fast decay O(vertical bar x vertical bar(2)(s -)(N)). This result is the extension of the work by Davila, del Pino, Musso and Wei (2008, Cak. Var. Partial Differ. Equ. 32, no. 4, 453-480) to the fractional case.

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《Proceedings of the Royal Society of Edinburgh, Section A. Mathematics》 |2022年第1期|28-53|共26页
作者
Ao Weiwei; Liu Chao; Wang Liping;
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作者单位

Wuhan Univ;

East China Normal Univ;

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正文语种英语
中图分类数学;
关键词
Fractional elliptic problems; supercritical cases; existence; SCHRODINGER-EQUATION; POSITIVE SOLUTIONS; NONDEGENERACY; UNIQUENESS; STATES;

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Fast and slow decay solutions for supercritical fractional elliptic problems in exterior domains

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