Asymptotic profile and Morse index of the radial solutions of the Hénon equation

2021 ◽  
Vol 287 ◽  
pp. 212-235
Author(s):  
Wendel Leite da Silva ◽  
Ederson Moreira dos Santos
Keyword(s):  
Morse Index ◽  
Radial Solutions ◽  
Asymptotic Profile ◽  
Hénon Equation

scholarly journals The asymptotically linear Hénon problem

2020 ◽  
pp. 2050042
Author(s):  
Anna Lisa Amadori
Keyword(s):  
Boundary Conditions ◽  
Morse Index ◽  
Dirichlet Boundary ◽  
Dirichlet Boundary Conditions ◽  
Radial Solutions ◽  
Asymptotically Linear ◽  
Planar Case ◽  
Asymptotic Profile ◽  
Least Energy Solutions ◽  
Least Energy

In this paper, we consider the Hénon problem in the ball with Dirichlet boundary conditions. We study the asymptotic profile of radial solutions and then deduce the exact computation of their Morse index when the exponent [Formula: see text] is close to [Formula: see text]. Next we focus on the planar case and describe the asymptotic profile of some solutions which minimize the energy among functions which are invariant for reflection and rotations of a given angle [Formula: see text]. By considerations based on the Morse index we see that, depending on the values of [Formula: see text] and [Formula: see text], such least energy solutions can be radial, or nonradial and different one from another.

scholarly journals A Morse index formula for radial solutions of Lane–Emden problems

2017 ◽  
Vol 322 ◽  
pp. 682-737 ◽  
Author(s):  
Francesca De Marchis ◽  
Isabella Ianni ◽  
Filomena Pacella
Keyword(s):  
Morse Index ◽  
Index Formula ◽  
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.

scholarly journals Non radial solutions for a non homogeneous Hénon equation

2014 ◽  
Vol 109 ◽  
pp. 45-55 ◽  
Author(s):  
M. Badiale ◽  
G. Cappa
Keyword(s):  
Radial Solutions ◽  
Hénon Equation

scholarly journals A note on the radial solutions for the supercritical Hénon equation

2008 ◽  
Vol 341 (1) ◽  
pp. 720-728 ◽  
Author(s):  
Vivina Barutello ◽  
Simone Secchi ◽  
Enrico Serra
Keyword(s):  
Radial Solutions ◽  
Hénon Equation
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