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Radially Symmetric Solutions of Δw+wp−1w=0
Joint Authors
Troy, William C.
Krisner, Edward P.
Source
International Journal of Differential Equations
Issue
Vol. 2012, Issue 2012 (31 Dec. 2012), pp.1-34, 34 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2012-10-04
Country of Publication
Egypt
No. of Pages
34
Main Subjects
Abstract EN
We investigate solutions of w′′+N−1/rw′+wp−1w=0, r>0 and focus on the regime N>2 and p>N/(N-2).
Our advance is to develop a technique to efficiently classify the behavior of solutions on (rmin,rmax), their maximal positive interval of existence.
Our approach is to transform the nonautonomous w equation into an autonomous ODE.
This reduces the problem to analyzing the phase plane of the autonomous equation.
We prove the existence of new families of solutions of the w equation and describe their asymptotic behavior.
In the subcritical case N/(N-2)
Our advance is to prove the existence of a family of solutions of the subcritical case which satisfiesw(ri)=w1(ri) for infinitely many values ri>0.
At the critical value p=(N+2)/(N-2) there is a continuum of positive singular solutions, and a continuum of sign changing singular solutions.
In the supercritical regime p>(N+2)/(N-2) we prove the existence of a family of “super singular” sign changing singular solutions.
American Psychological Association (APA)
Troy, William C.& Krisner, Edward P.. 2012. Radially Symmetric Solutions of Δw+wp−1w=0. International Journal of Differential Equations،Vol. 2012, no. 2012, pp.1-34.
https://search.emarefa.net/detail/BIM-461340
Modern Language Association (MLA)
Troy, William C.& Krisner, Edward P.. Radially Symmetric Solutions of Δw+wp−1w=0. International Journal of Differential Equations No. 2012 (2012), pp.1-34.
https://search.emarefa.net/detail/BIM-461340
American Medical Association (AMA)
Troy, William C.& Krisner, Edward P.. Radially Symmetric Solutions of Δw+wp−1w=0. International Journal of Differential Equations. 2012. Vol. 2012, no. 2012, pp.1-34.
https://search.emarefa.net/detail/BIM-461340
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-461340