A Morse index formula for minimax type saddle points by a Ljusternik–Schnirelman minimax algorithm and its application in computation of multiple solutions of semilinear elliptic equation

2021 ◽  
Vol 382 ◽  
pp. 113076
Author(s):  
Xudong Yao ◽  
Zhujun Li
Keyword(s):  
Elliptic Equation ◽  
Multiple Solutions ◽  
Morse Index ◽  
Saddle Points ◽  
Semilinear Elliptic Equation ◽  
Index Formula ◽  
Semilinear Elliptic

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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