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Boundedness, periodicity, and convergence of solutions in a retarded Liénard equation. (English) Zbl 0803.34064

From authors’ introduction: “The paper deals with the retarded Liénard equation

x '' +f(x)x ' +g(x(t-h))=e(t),(*)

where h0 is the delay and e is a bounded function. With appropriate assumptions on f and g the authors obtain necessary and sufficient conditions for solutions of (*) to be uniformly ultimately bounded. Thus by a fixed point theorem, those conditions imply that (*) has a T-periodic solution whenever e is T-periodic. Also are given conditions under which all solutions of (*) converge.

MSC:
34K99Functional-differential equations
34C11Qualitative theory of solutions of ODE: growth, boundedness
34C25Periodic solutions of ODE
34D40Ultimate boundedness (MSC2000)
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