Existence results for the positive solutions of nonlinear elliptic systems

2004 ◽  
Vol 153 (3) ◽  
pp. 833-842 ◽  
Author(s):  
Jihui Zhang
Keyword(s):  
Positive Solutions ◽  
Elliptic Systems ◽  
Existence Results ◽  
Nonlinear Elliptic Systems ◽  
Nonlinear Elliptic

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.

Existence results for some nonlinear elliptic systems

2009 ◽  
Vol 71 (7-8) ◽  
pp. 2840-2846 ◽  
Author(s):  
Jihui Zhang ◽  
Zhitao Zhang
Keyword(s):  
Elliptic Systems ◽  
Existence Results ◽  
Nonlinear Elliptic Systems ◽  
Nonlinear Elliptic

scholarly journals Existence results of positive solutions for nonlinear cooperative elliptic systems involving fractional Laplacian

2018 ◽  
Vol 20 (03) ◽  
pp. 1750032 ◽  
Author(s):  
Alexander Quaas ◽  
Aliang Xia
Keyword(s):  
Positive Solutions ◽  
Fractional Laplacian ◽  
Degree Theory ◽  
Elliptic Systems ◽  
Existence Results ◽  
Nonlinear Elliptic Problem ◽  
Topological Degree Theory ◽  
Scaling Method ◽  
Smooth Bounded Domain ◽  
Nonlinear Elliptic

In this paper, we prove existence results of positive solutions for the following nonlinear elliptic problem with gradient terms: [Formula: see text] where [Formula: see text] denotes the fractional Laplacian and [Formula: see text] is a smooth bounded domain in [Formula: see text]. It shown that under some assumptions on [Formula: see text] and [Formula: see text], the problem has at least one positive solution [Formula: see text]. Our proof is based on the classical scaling method of Gidas and Spruck and topological degree theory.

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