On a variational problem for radial solutions to extremal elliptic equations

2008 ◽  
Vol 188 (2) ◽  
pp. 187-206
Author(s):  
Orazio Arena ◽  
Pasquale Buonocore
Keyword(s):  
Variational Problem ◽  
Elliptic Equations ◽  
Radial Solutions

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

scholarly journals Structure Results for Semilinear Elliptic Equations with Hardy Potentials

2018 ◽  
Vol 18 (1) ◽  
pp. 65-85 ◽  
Author(s):  
Matteo Franca ◽  
Maurizio Garrione
Keyword(s):  
Dynamical System ◽  
Invariant Manifold ◽  
Elliptic Equations ◽  
Semilinear Elliptic Equations ◽  
Complete Picture ◽  
Radial Solutions ◽  
Semilinear Elliptic ◽  
Slow Decay ◽  
Manifold Theory ◽  
Semilinear Problem

AbstractWe prove structure results for the radial solutions of the semilinear problem\Delta u+\frac{\lambda(|x|)}{|x|^{2}}u+f(u(x),|x|)=0,where λ is afunctionandfis superlinear in theu-variable. As particular cases, we are able to deal with Matukuma potentials and with nonlinearitiesfhaving different polynomial behaviors at zero and at infinity. We give the complete picture for the subcritical, critical and supercritical cases. The technique relies on the Fowler transformation, allowing to deal with a dynamical system in{{\mathbb{R}}^{3}}, for which elementary invariant manifold theory allows to draw the conclusions involving regular/singular and fast/slow-decay solutions.

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.

Sign in / Sign up

Export Citation Format

Share Document