scholarly journals On a class of nonlinear elliptic equations with fast increasing weight and critical growth

2010 ◽  
Vol 249 (5) ◽  
pp. 1035-1055 ◽  
Author(s):  
Marcelo F. Furtado ◽  
Olímpio H. Myiagaki ◽  
João Pablo P. da Silva
Keyword(s):  
Elliptic Equations ◽  
Nonlinear Elliptic Equations ◽  
Critical Growth ◽  
Nonlinear Elliptic

scholarly journals FOUNTAIN-LIKE SOLUTIONS FOR NONLINEAR ELLIPTIC EQUATIONS WITH CRITICAL GROWTH AND HARDY POTENTIAL

2005 ◽  
Vol 07 (06) ◽  
pp. 867-904 ◽  
Author(s):  
VERONICA FELLI ◽  
SUSANNA TERRACINI
Keyword(s):  
Elliptic Equation ◽  
Elliptic Equations ◽  
Nonlinear Elliptic Equation ◽  
Blow Up ◽  
Nonlinear Elliptic Equations ◽  
Critical Growth ◽  
Hardy Potential ◽  
Nonlinear Elliptic ◽  
Hardy Type ◽  
Type Potential

We prove the existence of fountain-like solutions, obtained by superposition of bubbles of different blow-up orders, for a nonlinear elliptic equation with critical growth and Hardy-type potential.

Strict convexity of level sets of solutions of some nonlinear elliptic equations

2004 ◽  
Vol 134 (2) ◽  
pp. 363-373 ◽  
Author(s):  
Francesca Gladiali ◽  
Massimo Grossi
Keyword(s):  
Elliptic Equations ◽  
Level Sets ◽  
Nonlinear Elliptic Equations ◽  
Gauss Curvature ◽  
Strict Convexity ◽  
Critical Growth ◽  
Strictly Convex ◽  
Nonlinear Elliptic ◽  
Suitable Function ◽  
Image Position

In this paper we study the convexity of the level sets of solutions of the problem where f is a suitable function with subcritical or critical growth. Under some assumptions on the Gauss curvature of ∂Ω, we prove that the level sets of the solution of (0.1) are strictly convex.

A new concept of reduced measure for nonlinear elliptic equations

2004 ◽  
Vol 339 (3) ◽  
pp. 169-174 ◽  
Author(s):  
Haïm Brezis ◽  
Moshe Marcus ◽  
Augusto C. Ponce
Keyword(s):  
Elliptic Equations ◽  
Nonlinear Elliptic Equations ◽  
Nonlinear Elliptic
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