On the Critical Case in Oscillation for Differential Equations with a Single Delay and with Several Delays | Zendy

Jaromír Baštinec | Zendy; Leonid Berezansky | Zendy; Josef Diblı́k | Zendy; Zdeněk Šmarda | Zendy

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On the Critical Case in Oscillation for Differential Equations with a Single Delay and with Several Delays

Author(s) -

Jaromír Baštinec,

Leonid Berezansky,

Josef Diblı́k,

Zdeněk Šmarda

Publication year - 2010

Publication title -

abstract and applied analysis

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.228

H-Index - 56

eISSN - 1687-0409

pISSN - 1085-3375

DOI - 10.1155/2010/417869

Subject(s) - mathematics , delay differential equation , oscillation (cell signaling) , mathematical analysis , scalar (mathematics) , differential equation , distributed parameter system , geometry , genetics , biology

New nonoscillation and oscillation criteria are derived for scalar delay differential equations ̇()+()(ℎ())=0,()≥0,ℎ()≤,≥0, and ∑̇()+=1()(ℎ())=0,()≥0,ℎ()≤, and ≥0, in the critical case including equations with several unbounded delays,without the usual assumption that the parameters ,ℎ,, and ℎ of the equations are continuous functions. These conditions improve and extend some known oscillation results in the critical case for delay differential equations

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