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A note on periodic solutions of nonautonomous second-order systems. (English) Zbl 1055.34084

The authors study the multiplicity of periodic solutions for the second-order equation \[ \ddot u + \nabla F(t,u) = e(t),\quad u\in\mathbb R^n, \] where the function \(F\) is periodic in the first \(r\) components of \(u\) and subquadratically in the other \(n-r\) components. Using minimax methods, they show that there are at least \(r+1\) geometrically distinct periodic solutions.
Reviewer: Bin Liu (Beijing)

MSC:

34C25 Periodic solutions to ordinary differential equations
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