Stability conditions of zero solution for third order differential equation in critical case

Abstract EN

In this paper, we study the conditions under which the zero solution is stable in the semi- liner case for certain third order differential equation of the form : ( ) ( ) ( ) ( , , , ) 1 2 3 y′′′ + p t y′′ + p t y′ + p t y = h t y y′ y′′ Where w t C , s = 1,2,3 s q C , ( ) : → s p [q w (t )] , ∈ s s s s = π + t ∈ = [a,∞) , a ∈ N The characteristic equation of the above differential equation has complex roots of the form : 0 and the other root has the following 0 , λ > 1 2 0 λ = −λ = iλ Re, 0 .

3 property λ < −M M >