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) \(x'''+\alpha x''+bx'+f(x(t-r))=p(t)\), (2) \(x'''+\alpha x''+\varphi(x(t-r))+f(x)=p(t)\). Here \(r,a,b\) are positive constants, \(f(x)\), \(\varphi(x)\), \(p(t)\) are continuous functions, \(f(0)=\varphi(0)\). 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.
Reviewer: A.Slavova (Russe)


34K20 Stability theory of functional-differential equations
34K99 Functional-differential equations (including equations with delayed, advanced or state-dependent argument)
34C25 Periodic solutions to ordinary differential equations