Existence and multiplicity of positive radial solutions for a semilinear elliptic equation with change of sign

2001 ◽  
Vol 80 (1-2) ◽  
pp. 65-77 ◽  
Author(s):  
Qingliu Yao
Keyword(s):  
Elliptic Equation ◽  
Semilinear Elliptic Equation ◽  
Radial Solutions ◽  
Existence And Multiplicity ◽  
Semilinear Elliptic ◽  
Positive Radial Solutions

Morse index and symmetry breaking for an elliptic equation with negative exponent in expanding annuli

2017 ◽  
Vol 147 (6) ◽  
pp. 1215-1232
Author(s):  
Zongming Guo ◽  
Linfeng Mei ◽  
Zhitao Zhang
Keyword(s):  
Elliptic Equation ◽  
Symmetry Breaking ◽  
Morse Index ◽  
Blow Up ◽  
Semilinear Elliptic Equation ◽  
Radial Solutions ◽  
Entire Solutions ◽  
Semilinear Elliptic ◽  
Image Position

Bifurcation of non-radial solutions from radial solutions of a semilinear elliptic equation with negative exponent in expanding annuli of ℝ2 is studied. To obtain the main results, we use a blow-up argument via the Morse index of the regular entire solutions of the equationThe main results of this paper can be seen as applications of the results obtained recently for finite Morse index solutions of the equationwith N ⩾ 2 and p > 0.

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