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Solutions périodiques des systèmes non conservatifs périodiquement perturbés. (Periodic solutions of periodically perturbed nonconservative systems). (French) Zbl 0607.34041

We use Fourier series method, Leray-Schauder’s techniques and coincidence degree in order to get existence and uniqueness results for \(2\pi\)- periodic solutions of the system \(x''(t)+Cx'(t)+\text{grad}_ xG(t,x(t))=e(t)\) under nonuniform conditions (in t). The eigenvalues of the Hessian of G may be contained in different gaps of the resolvent of the associated second order linear problem.

MSC:

34C25 Periodic solutions to ordinary differential equations
34B15 Nonlinear boundary value problems for ordinary differential equations
34B30 Special ordinary differential equations (Mathieu, Hill, Bessel, etc.)
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