Problems of periodic solutions for a type of Duffing equation with state-dependent delay. (English) Zbl 1196.34090

The authors deal with the following Duffing equation with state-dependent delay \[ x''(t)+g(x(t-\tau(t,x(t))))=p(t), \]
where \(g, p\in C(\mathbb R,\mathbb R)\) with \(p(t+T)=p(t)\), \(\tau\in C(\mathbb R^2,\mathbb R^+)\) with \(\tau(t+T,x)=\tau(t,x)\), \(T>0\) is a given constant and \(\mathbb R^+=[0,+\infty)\). By employing a continuation theorem of the coincidence degree theory, more general delay-dependent sufficient criteria are established for the existence of \(T\)-periodic solutions, which generalize some related results independent of the delay in the literature.


34K13 Periodic solutions to functional-differential equations
47N20 Applications of operator theory to differential and integral equations
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