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On stability, boundedness and existence of periodic solution of a kind of third order nonlinear delay differential system. (English) Zbl 0758.34072
Third order nonlinear differential equations with delay are considered: (1) x ''' +αx '' +bx ' +f(x(t-r))=p(t), (2) x ''' +αx '' +ϕ(x(t-r))+f(x)=p(t). Here r,a,b are positive constants, f(x), ϕ(x), p(t) are continuous functions, f(0)=ϕ(0). The stability of the zero solutions of (1) and (2) with p(t)=0 is studied. Sufficient conditions for uniform boundedness and uniform ultimate boundedness of the solution of (1) are given. The existence of periodic solutions when p(t) is a periodic function is discussed.
MSC:
34K20Stability theory of functional-differential equations
34K99Functional-differential equations
34C25Periodic solutions of ODE