Displaying similar documents to “On the oscillation of a class of linear homogeneous third order differential equations”

On oscillation and asymptotic property of a class of third order differential equations

N. Parhi, Seshadev Pardi (1999)

Czechoslovak Mathematical Journal

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In this paper, oscillation and asymptotic behaviour of solutions of y ' ' ' + a ( t ) y ' ' + b ( t ) y ' + c ( t ) y = 0 have been studied under suitable assumptions on the coefficient functions a , b , c C ( [ σ , ) , R ) , σ R , such that a ( t ) 0 , b ( t ) 0 and c ( t ) < 0 .

An integral condition of oscillation for equation y ' ' ' + p ( t ) y ' + q ( t ) y = 0 with nonnegative coefficients

Anton Škerlík (1995)

Archivum Mathematicum

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Our aim in this paper is to obtain a new oscillation criterion for equation y ' ' ' + p ( t ) y ' + q ( t ) y = 0 with a nonnegative coefficients which extends and improves some oscillation criteria for this equation. In the special case of equation (*), namely, for equation y ' ' ' + q ( t ) y = 0 , our results solve the open question of C h a n t u r i y a .

Some oscillation theorems for second order differential equations

Chung-Fen Lee, Cheh Chih Yeh, Chuen-Yu Gau (2005)

Czechoslovak Mathematical Journal

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In this paper we establish some oscillation or nonoscillation criteria for the second order half-linear differential equation ( r ( t ) Φ ( u ' ( t ) ) ) ' + c ( t ) Φ ( u ( t ) ) = 0 , where (i) r , c C ( [ t 0 , ) , : = ( - , ) ) and r ( t ) > 0 on [ t 0 , ) for some t 0 0 ; (ii) Φ ( u ) = | u | p - 2 u for some fixed number p > 1 . We also generalize some results of Hille-Wintner, Leighton and Willet.

Some properties of third order differential operators

Mariella Cecchi, Zuzana Došlá, Mauro Marini (1997)

Czechoslovak Mathematical Journal

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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).