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Radially Symmetric Solutions of a Nonlinear Elliptic Equation
Joint Authors
Troy, William C.
Krisner, Edward P.
Source
International Journal of Mathematics and Mathematical Sciences
Issue
Vol. 2011, Issue 2011 (31 Dec. 2011), pp.1-22, 22 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2011-07-13
Country of Publication
Egypt
No. of Pages
22
Main Subjects
Abstract EN
We investigate the existence and asymptotic behavior of positive, radially symmetric singular solutions of w′′+((N−1)/r)w′−|w|p−1w=0, r>0.
We focus on the parameter regime N>2 and 1
0.
Our advance is to develop a technique to efficiently classify the behavior of solutions which are positive on a maximal positive interval (rmin,rmax).
Our approach is to transform the nonautonomous w equation into an autonomous ODE.
This reduces the problem to analyzing the behavior of solutions in the phase plane of the autonomous equation.
We then show how specific solutions of the autonomous equation give rise to the existence of several new families of singular solutions of the w equation.
Specifically, we prove the existence of a family of singular solutions which exist on the entire interval (0,∞), and which satisfy 0
An important open problem for the nonautonomous equation is presented.
Its solution would lead to the existence of a new family of “super singular” solutions which lie entirely above w1(r).
American Psychological Association (APA)
Krisner, Edward P.& Troy, William C.. 2011. Radially Symmetric Solutions of a Nonlinear Elliptic Equation. International Journal of Mathematics and Mathematical Sciences،Vol. 2011, no. 2011, pp.1-22.
https://search.emarefa.net/detail/BIM-484762
Modern Language Association (MLA)
Krisner, Edward P.& Troy, William C.. Radially Symmetric Solutions of a Nonlinear Elliptic Equation. International Journal of Mathematics and Mathematical Sciences No. 2011 (2011), pp.1-22.
https://search.emarefa.net/detail/BIM-484762
American Medical Association (AMA)
Krisner, Edward P.& Troy, William C.. Radially Symmetric Solutions of a Nonlinear Elliptic Equation. International Journal of Mathematics and Mathematical Sciences. 2011. Vol. 2011, no. 2011, pp.1-22.
https://search.emarefa.net/detail/BIM-484762
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-484762