A Concentration Phenomenon for p-Laplacian Equation
Author
Source
Journal of Applied Mathematics
Issue
Vol. 2014, Issue 2014 (31 Dec. 2014), pp.1-6, 6 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2014-07-20
Country of Publication
Egypt
No. of Pages
6
Main Subjects
Abstract EN
It is proved that if the bounded function of coefficient Qn in the following equation -div {|∇u|p-2∇u}+V(x)|u|p-2u=Qn(x)|u|q-2u, u(x)=0 as x∈∂Ω. u(x)⟶0 as |x|⟶∞ is positive in a region contained in Ω and negative outside the region, the sets {Qn>0} shrink to a point x0∈Ω as n→∞, and then the sequence un generated by the nontrivial solution of the same equation, corresponding to Qn, will concentrate at x0 with respect to W01,p(Ω) and certain Ls(Ω)-norms.
In addition, if the sets {Qn>0} shrink to finite points, the corresponding ground states {un} only concentrate at one of these points.
These conclusions extend the results proved in the work of Ackermann and Szulkin (2013) for case p=2.
American Psychological Association (APA)
Zhong, Yansheng. 2014. A Concentration Phenomenon for p-Laplacian Equation. Journal of Applied Mathematics،Vol. 2014, no. 2014, pp.1-6.
https://search.emarefa.net/detail/BIM-449654
Modern Language Association (MLA)
Zhong, Yansheng. A Concentration Phenomenon for p-Laplacian Equation. Journal of Applied Mathematics No. 2014 (2014), pp.1-6.
https://search.emarefa.net/detail/BIM-449654
American Medical Association (AMA)
Zhong, Yansheng. A Concentration Phenomenon for p-Laplacian Equation. Journal of Applied Mathematics. 2014. Vol. 2014, no. 2014, pp.1-6.
https://search.emarefa.net/detail/BIM-449654
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-449654