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Solvability of the forced Duffing equation at resonance. (English) Zbl 0915.34032
The forced Duffing equation $u'(t)+ m^2\omega^2 u(t)+ g(u(t))= h(t),\quad t\in [0,T],\quad u(0)- u(T)= u'(0)- u'(T)= 0,$ with $$T>0$$, $$\omega= 2\pi/T$$, $$g\in C(\mathbb{R}, \mathbb{R})$$, and $$h\in L^1(0,T)$$, is considered. Using minimax methods a new solvability condition in both cases, $$m= 0$$ and $$m\geq 1$$, is obtained. Three theorems concerning these conditions are proved.

##### MSC:
 34C25 Periodic solutions to ordinary differential equations
##### Keywords:
forced Duffing equation
Full Text:
##### References:
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