Radial Solutions of a Supercritical Elliptic Equation with Hardy Potential

2012 ◽  
Vol 12 (1) ◽  
Author(s):  
Zuji Guo ◽  
Zhaoli Liu
Keyword(s):  
Elliptic Equation ◽  
Radial Solutions ◽  
Hardy Potential

AbstractVarious properties of radial solutions of the supercritical elliptic equation with Hardy Potentialare studied, where Ω = int{x ∈ ℝ

Existence of Radial Solutions for Quasilinear Elliptic Equations with Singular Nonlinearities

2003 ◽  
Vol 3 (4) ◽  
Author(s):  
Beatrice Acciaio ◽  
Patrizia Pucci
Keyword(s):  
Elliptic Equation ◽  
Elliptic Equations ◽  
Quasilinear Elliptic Equation ◽  
Quasilinear Elliptic Equations ◽  
Radial Solutions ◽  
Singular Nonlinearities ◽  
Quasilinear Elliptic

AbstractWe prove the existence of radial solutions of the quasilinear elliptic equation div(A(|Du|)Du) + f(u) = 0 in ℝ

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.

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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