scholarly journals Concentration profile, energy, and weak limits of radial solutions to semilinear elliptic equations with Trudinger–Moser critical nonlinearities

2021 ◽  
Vol 60 (2) ◽  
Author(s):  
Daisuke Naimen
Keyword(s):  
Concentration Profile ◽  
Elliptic Equations ◽  
Semilinear Elliptic Equations ◽  
Radial Solutions ◽  
Critical Nonlinearities ◽  
Semilinear Elliptic ◽  
Weak Limits

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.

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