Positive solutions for weakly coupled nonlinear elliptic systems

2010 ◽  
Vol 30 (5) ◽  
pp. 1577-1592 ◽  
Author(s):  
Long Jing ◽  
Yang Jianfu
Keyword(s):  
Positive Solutions ◽  
Elliptic Systems ◽  
Nonlinear Elliptic Systems ◽  
Nonlinear Elliptic ◽  
Weakly Coupled

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.

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