scholarly journals Schwarz symmetrization and comparison results for nonlinear elliptic equations and eigenvalue problems

2012 ◽  
Vol 192 (6) ◽  
pp. 987-1024 ◽  
Author(s):  
Leonardo Prange Bonorino ◽  
José Fábio Bezerra Montenegro
Keyword(s):  
Elliptic Equations ◽  
Eigenvalue Problems ◽  
Nonlinear Elliptic Equations ◽  
Nonlinear Elliptic ◽  
Schwarz Symmetrization ◽  
Comparison Results

On the viscosity solutions of eigenvalue problems for a class of nonlinear elliptic equations

2019 ◽  
Vol 12 (4) ◽  
pp. 393-421
Author(s):  
Tilak Bhattacharya ◽  
Leonardo Marazzi
Keyword(s):  
Viscosity Solutions ◽  
Elliptic Equations ◽  
Eigenvalue Problems ◽  
A Priori ◽  
Nonlinear Elliptic Equations ◽  
First Eigenvalue ◽  
Nonlinear Elliptic ◽  
Degenerate Elliptic ◽  
First Eigenfunction ◽  
Nonlinear Degenerate

AbstractWe consider viscosity solutions of a class of nonlinear degenerate elliptic equations, involving a parameter, on bounded domains. These arise in the study of eigenvalue problems. We prove comparison principles and a priori supremum bounds for the solutions. We also address the eigenvalue problem and, in many instances, show the existence of the first eigenvalue and an associated positive first eigenfunction.

scholarly journals Positive Solutions of Nonlinear Elliptic Equations with Nonlinear Boundary Conditions

2013 ◽  
Vol 2013 ◽  
pp. 1-6
Author(s):  
Hua Luo
Keyword(s):  
Boundary Conditions ◽  
Positive Solutions ◽  
Elliptic Equations ◽  
Nonlinear Boundary ◽  
Eigenvalue Problems ◽  
Nonlinear Elliptic Equations ◽  
Nonlinear Boundary Conditions ◽  
Nonlinear Elliptic ◽  
Elliptic Eigenvalue Problems ◽  
Bifurcation From Interval

This paper discusses bifurcation from interval for the elliptic eigenvalue problems with nonlinear boundary conditions and studies the behavior of the bifurcation components.

Eigenvalue problems for nonlinear elliptic equations with unilateral constraints

2008 ◽  
Vol 69 (1) ◽  
pp. 85-109 ◽  
Author(s):  
Michael E. Filippakis ◽  
Nikolaos S. Papageorgiou ◽  
Vasile Staicu
Keyword(s):  
Elliptic Equations ◽  
Eigenvalue Problems ◽  
Nonlinear Elliptic Equations ◽  
Unilateral Constraints ◽  
Nonlinear Elliptic

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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