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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
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