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Nodal vector solutions with clustered peaks for nonlinear elliptic equations in ℝ3

Part of: Elliptic equations and systems Partial differential equations

Published online by Cambridge University Press:  01 July 2016

Qihan He  and
Chunhua Wang
Qihan He
Affiliation:
School of Mathematics and Statistics and Hubei Key Laboratory of Mathematical Sciences, Central China Normal University, Wuhan 430079, People's Republic of China(, [email protected]; , [email protected])
Chunhua Wang*
Affiliation:
School of Mathematics and Statistics and Hubei Key Laboratory of Mathematical Sciences, Central China Normal University, Wuhan 430079, People's Republic of China(, [email protected]; , [email protected])
*
†Corresponding author.
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Extract

We study the following coupled nonlinear Schr¨odinger system in ℝ3:

where μ1 > 0, μ2 > 0 and β ∈ ℝ is a coupling constant. Irrespective of whether the system is repulsive or attractive, we prove that it has nodal semi-classical segregated or synchronized bound states with clustered spikes for sufficiently small ε under some additional conditions on P(x), Q(x) and β. Moreover, the number of this type of solutions will go to infinity as ε → 0+.

Keywords

clustered peaksnodal vector solutionsnonlinear coupled equations

MSC classification

Secondary: 35J10: Schrödinger operator 35B99: None of the above, but in this section 35J60: Nonlinear elliptic equations
Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 146 , Issue 5 , October 2016 , pp. 947 - 982
Copyright
Copyright © Royal Society of Edinburgh 2016 

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