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November/December 2017 Existence, non-degeneracy of proportional positive solutions and least energy solutions for a fractional elliptic system
Qihan He, Shuangjie Peng, Yanfang Peng
Adv. Differential Equations 22(11/12): 867-892 (November/December 2017).

Abstract

In this paper, we study the following fractional nonlinear Schrödinger system $$ \left\{ \begin{array}{ll} (-\Delta)^s u +u=\mu_1 |u|^{2p-2}u+\beta |v|^p|u|^{p-2}u, ~~x\in \mathbb R^N, \\ (-\Delta)^s v +v=\mu_2 |v|^{2p-2}v+\beta |u|^p|v|^{p-2}v, ~~x\in \mathbb R^N, \end{array} \right. $$ where $0 < s < 1, \mu_1 > 0, \mu_2 > 0, 1 < p < 2_s^*/2, 2_s^*=+\infty$ for $N\le 2s$ and $2_s^*=2N/(N-2s)$ for $N > 2s$, and $\beta \in \mathbb R$ is a coupling constant. We investigate the existence and non-degeneracy of proportional positive vector solutions for the above system in some ranges of $\mu_1,\mu_2, p, \beta$. We also prove that the least energy vector solutions must be proportional and unique under some additional assumptions.

Citation

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Qihan He. Shuangjie Peng. Yanfang Peng. "Existence, non-degeneracy of proportional positive solutions and least energy solutions for a fractional elliptic system." Adv. Differential Equations 22 (11/12) 867 - 892, November/December 2017.

Information

Published: November/December 2017
First available in Project Euclid: 1 September 2017

zbMATH: 1377.35264
MathSciNet: MR3692913

Subjects:
Primary: 35A01, 35A20, 35J60

Rights: Copyright © 2017 Khayyam Publishing, Inc.

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Vol.22 • No. 11/12 • November/December 2017
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