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Some oscillation theorems for second order differential equations

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

Czechoslovak Mathematical Journal

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 integral curves in a neighbourhood of planar singular points

Shu-Xiang Yu, Chengfu Jin (1984)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

Si studia l'andamento delle traiettorie di un sistema dinamico piano rappresentato dalle equazioni (1) del testo, nell'intorno di un punto singolare isolato.

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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