scholarly journals Multiple solutions to weakly coupled supercritical elliptic systems

2019 ◽  
Vol 198 (4) ◽  
pp. 1243-1255 ◽  
Author(s):  
Omar Cabrera ◽  
Mónica Clapp
Keyword(s):  
Multiple Solutions ◽  
Elliptic Systems ◽  
Weakly Coupled

Positivity for elliptic and parabolic systems

1978 ◽  
Vol 79 (3-4) ◽  
pp. 183-191 ◽  
Author(s):  
J. F. G. Auchmuty
Keyword(s):  
Initial Conditions ◽  
Elliptic Systems ◽  
Reaction Diffusion ◽  
Parabolic Systems ◽  
Initial Boundary ◽  
Reaction Diffusion Equations ◽  
Biological Phenomena ◽  
Weakly Coupled ◽  
Coupling Terms ◽  
Initial Boundary Value

SynopsisThe positivity of solutions of initial-boundary value problems for weakly-coupled semilinear parabolic or elliptic systems of equations is studied. Conditions on the coupling terms are described which ensure that the solutions of the parabolic systems remain positive whenever the initial conditions are positive. For elliptic systems involving a parameter, conditions on the coupling terms are described which imply that solution branches which contain a positive solution, in fact, contain only positive solutions. Applications of these theorems to certain reaction-diffusion equations arising in the modelling of biological phenomena are given.

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