## 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.

### MSC:

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

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