Construction of Nodal Bubbling Solutions for the Weighted Sinh-Poisson Equation
Joint Authors
Source
Issue
Vol. 2013, Issue 2013 (31 Dec. 2013), pp.1-16, 16 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2013-11-27
Country of Publication
Egypt
No. of Pages
16
Main Subjects
Abstract EN
We consider the weighted sinh-Poisson equation Δu+2ε2|x|2αsinh u=0 in B1(0), u=0 on ∂B1(0), where ε>0 is a small parameter, α∈(-1,+∞)∖{0}, and B1(0) is a unit ball in ℝ2.
By a constructive way, we prove that for any positive integer m, there exists a nodal bubbling solution uε which concentrates at the origin and the other m-points q~l=(λ cos (2π(l−1)/m),λ sin (2π(l−1)/m)), l=2,…,m+1, such that as ε→0, 2ε2|x|2αsinh uε⇀8π(1+α)δ0+∑l=2m+18π(−1)l−1δq~l, where λ∈(0,1) and m is an odd integer with (1+α)(m+2)-1>0, or m is an even integer.
The same techniques lead also to a more general result on general domains.
American Psychological Association (APA)
Zhang, Yibin& Yang, Haitao. 2013. Construction of Nodal Bubbling Solutions for the Weighted Sinh-Poisson Equation. Abstract and Applied Analysis،Vol. 2013, no. 2013, pp.1-16.
https://search.emarefa.net/detail/BIM-505241
Modern Language Association (MLA)
Zhang, Yibin& Yang, Haitao. Construction of Nodal Bubbling Solutions for the Weighted Sinh-Poisson Equation. Abstract and Applied Analysis No. 2013 (2013), pp.1-16.
https://search.emarefa.net/detail/BIM-505241
American Medical Association (AMA)
Zhang, Yibin& Yang, Haitao. Construction of Nodal Bubbling Solutions for the Weighted Sinh-Poisson Equation. Abstract and Applied Analysis. 2013. Vol. 2013, no. 2013, pp.1-16.
https://search.emarefa.net/detail/BIM-505241
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-505241