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July/August 2020 Multi-bump solutions for fractional Schrödinger equation with electromagnetic fields and critical nonlinearity
Sihua Liang, Nguyen Thanh Chung, Binlin Zhang
Adv. Differential Equations 25(7/8): 423-456 (July/August 2020).

Abstract

In this article, we consider the existence of multi-bump solutions for a class of the fractional Schrödinger equation with external magnetic field and critical nonlinearity in $\mathbb{R}^N$: $$(-\Delta)_A^su + (\lambda V(x) + Z(x))u = \beta f(|u|^2)u + |u|^{2_s^\ast-2}u,$$ where $f$ is a continuous function satisfying Ambrosetti-Rabinowitz condition, and $V: \mathbb{R}^N \rightarrow\mathbb{R}$ has a potential well $\Omega := \mbox{int}V^{-1}(0)$ which possesses $k$ disjoint bounded components $\Omega := \cup_{j=1}^k\Omega_j$. By using variational methods, we prove that if the parameter $\lambda > 0$ is large enough, then the equation has at least $2^k-1$ multi-bump solutions.

Citation

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Sihua Liang. Nguyen Thanh Chung. Binlin Zhang. "Multi-bump solutions for fractional Schrödinger equation with electromagnetic fields and critical nonlinearity." Adv. Differential Equations 25 (7/8) 423 - 456, July/August 2020.

Information

Published: July/August 2020
First available in Project Euclid: 14 July 2020

zbMATH: 07243149
MathSciNet: MR4122515

Subjects:
Primary: 35B99, 35J10, 35J60, 47G20

Rights: Copyright © 2020 Khayyam Publishing, Inc.

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Vol.25 • No. 7/8 • July/August 2020
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