Multiple Positive Radial Solutions of Elliptic Equations in an Exterior Domain

2006 ◽  
Vol 148 (3) ◽  
pp. 217-228 ◽  
Author(s):  
Guodong Han ◽  
Jianjun Wang
Keyword(s):  
Elliptic Equations ◽  
Exterior Domain ◽  
Radial Solutions ◽  
Positive Radial Solutions

scholarly journals Three Solutions Theorem forp-Laplacian Problems with a Singular Weight and Its Application

2014 ◽  
Vol 2014 ◽  
pp. 1-9
Author(s):  
Yong-Hoon Lee ◽  
Seong-Uk Kim ◽  
Eun Kyoung Lee
Keyword(s):  
Exterior Domain ◽  
Upper And Lower Solutions ◽  
Solution Space ◽  
Combustion Model ◽  
Radial Solutions ◽  
Three Solutions ◽  
Singular Weight ◽  
One Dimensional ◽  
Positive Radial Solutions ◽  
Three Solutions Theorem

We prove Amann type three solutions theorem for one dimensionalp-Laplacian problems with a singular weight function. To prove this theorem, we define a strong upper and lower solutions and compute the Leray-Schauder degree on a newly established weighted solution space. As an application, we consider the combustion model and show the existence of three positive radial solutions on an exterior domain.

Positive solutions of elliptic equations involving supercritical growth

1991 ◽  
Vol 118 (1-2) ◽  
pp. 49-62 ◽  
Author(s):  
F. Merle ◽  
L. A. Peletier
Keyword(s):  
Elliptic Equation ◽  
Positive Solutions ◽  
Elliptic Equations ◽  
Singular Solution ◽  
Supremum Norm ◽  
Radial Solutions ◽  
Positive Radial Solutions

SynopsisPositive radial solutions of elliptic equation involving supercritical growth are analysed as their supremum norm tends to infinity. It is shown that they converge, uniformly away from the origin, as well as in H1, to the unique singular solution.

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