scholarly journals Symmetry of components, Liouville-type theorems and classification results for some nonlinear elliptic systems

2015 ◽  
Vol 35 (12) ◽  
pp. 5869-5877 ◽  
Author(s):  
Alberto Farina
Keyword(s):  
Elliptic Systems ◽  
Nonlinear Elliptic Systems ◽  
Liouville Type ◽  
Nonlinear Elliptic ◽  
Liouville Type Theorems

POSITIVE SOLUTIONS OF NONLINEAR ELLIPTIC SYSTEMS

1993 ◽  
Vol 03 (06) ◽  
pp. 823-837 ◽  
Author(s):  
A. CAÑADA ◽  
J.L. GÁMEZ
Keyword(s):  
Positive Solutions ◽  
Nonlinear Interaction ◽  
Spatial Dependence ◽  
Global Bifurcation ◽  
Elliptic Systems ◽  
Nonlinear Elliptic Systems ◽  
Decoupling Method ◽  
Nonlinear Elliptic ◽  
Cooperative Models

In this paper we prove the existence of nonnegative and non-trivial solutions of problems of the form [Formula: see text] Our main result improves many previous results of other authors and it may be applied to study the three standard situations: competition, prey-predator and cooperative models. We also cover some other cases which, due essentially to the spatial dependence or to a nonlinear interaction, are not any of these three types. The method of proof combines a decoupling method with a global bifurcation result.

Sign in / Sign up

Export Citation Format

Share Document