Anisotropic nonlinear elliptic systems with variable exponents and degenerate coercivity

2019 ◽  
pp. 1-21
Author(s):  
Naceri Mokhtar ◽  
Fares Mokhtari
Keyword(s):  
Elliptic Systems ◽  
Variable Exponents ◽  
Nonlinear Elliptic Systems ◽  
Nonlinear Elliptic ◽  
Degenerate Coercivity

scholarly journals Nonlinear elliptic systems with variable exponents and measure data

2015 ◽  
Vol 1 (2) ◽  
pp. 108-125 ◽  
Author(s):  
Mostafa Bendahmane ◽  
Fares Mokhtari
Keyword(s):  
Sobolev Spaces ◽  
Elliptic Systems ◽  
Existence Results ◽  
Measure Data ◽  
Variable Exponents ◽  
Nonlinear Elliptic Systems ◽  
Marcinkiewicz Spaces ◽  
Nonlinear Elliptic ◽  
Distributional Solutions ◽  
Functional Setting

Abstract In this paper we prove existence results for distributional solutions of nonlinear elliptic systems with a measure data. The functional setting involves Lebesgue-Sobolev spaces as well as weak Lebesgue (Marcinkiewicz) spaces with variable exponents W01,p(·)(Ω) and Mp(·)(Ω) respectively.

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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