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Radially Symmetric Solutions of

Troy, William C. and Krisner, Edward P. (2012) Radially Symmetric Solutions of. International Journal of Differential Equations, 2012. pp. 1-34. ISSN 1687-9643

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We investigate solutions of and focus on the regime and . Our advance is to develop a technique to efficiently classify the behavior of solutions on , their maximal positive interval of existence. Our approach is to transform the nonautonomous 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 equation and describe their asymptotic behavior. In the subcritical case there is a well-known closed-form singular solution, , such that as and as . Our advance is to prove the existence of a family of solutions of the subcritical case which satisfies for infinitely many values . At the critical value there is a continuum of positive singular solutions, and a continuum of sign changing singular solutions. In the supercritical regime we prove the existence of a family of “super singular” sign changing singular solutions.


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Item Type: Article
Status: Published
CreatorsEmailPitt UsernameORCID
Troy, William
Krisner, Edward
Date: 2012
Date Type: Publication
Journal or Publication Title: International Journal of Differential Equations
Volume: 2012
Publisher: Hindawi Limited
Page Range: pp. 1-34
DOI or Unique Handle: 10.1155/2012/296591
Schools and Programs: Dietrich School of Arts and Sciences > Mathematics
Refereed: Yes
ISSN: 1687-9643
Official URL:
Article Type: Research Article
Date Deposited: 13 May 2020 16:49
Last Modified: 13 May 2020 16:49


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