scholarly journals Liouville's theorem for first-order partial differential operators

1979 ◽  
Vol 41 (1) ◽  
pp. 117-121
Author(s):  
L. R. Hunt ◽  
J. J. Murray ◽  
M. J. Strauss
Keyword(s):  
Differential Operators ◽  
Partial Differential ◽  
First Order ◽  
Partial Differential Operators ◽  
Liouville’S Theorem

scholarly journals On Certain Proximities and Preorderings on the Transposition Hypergroups of Linear First-Order Partial Differential Operators

2014 ◽  
Vol 22 (1) ◽  
pp. 85-103 ◽  
Author(s):  
Jan Chvalina ◽  
Šárka Hošková-Mayerová
Keyword(s):  
Differential Operators ◽  
Partial Differential ◽  
First Order ◽  
Ordered Groups ◽  
Partial Differential Operators ◽  
Power Set

AbstractThe contribution aims to create hypergroups of linear first-order partial differential operators with proximities, one of which creates a tolerance semigroup on the power set of the mentioned differential operators. Constructions of investigated hypergroups are based on the so called “Ends-Lemma” applied on ordered groups of differnetial operators. Moreover, there is also obtained a regularly preordered transpositions hypergroup of considered partial differntial operators.

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