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Some classes of linear n th-order differential equations

Valter Šeda (1997)

Archivum Mathematicum

Sufficient conditions for the n -th order linear differential equation are derived which guarantee that its Cauchy function K , together with its derivatives i K t i , i = 1 , , n - 1 , is of constant sign. These conditions determine four classes of the linear differential equations. Further properties of these classes are investigated.

Some properties of third order differential operators

Mariella Cecchi, Zuzana Došlá, Mauro Marini (1997)

Czechoslovak Mathematical Journal

Consider the third order differential operator L given by L ( · ) 1 a 3 ( t ) d d t 1 a 2 ( t ) d d t 1 a 1 ( t ) d d t ( · ) and the related linear differential equation L ( x ) ( t ) + x ( t ) = 0 . We study the relations between L , its adjoint operator, the canonical representation of L , the operator obtained by a cyclic permutation of coefficients a i , i = 1 , 2 , 3 , in L and the relations between the corresponding equations. We give the commutative diagrams for such equations and show some applications (oscillation, property A).

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