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Periodic solutions of a class of Birkhoffian equations. (Chinese. English summary) Zbl 0903.58028

Summary: This paper discusses a class of Birkhoffian equations appearing in the research of modern mechanics: \[ D(t) \dot x+\varepsilon C'(t)x +B'_x(t,x) =0, \] where \(D(t)= (A-A^T)+ \varepsilon (C(t)- C^T(t))\), \(A-A^T\) is a \(2n \times 2n\) invertible matrix, \(C(t)\) and \(B(t,x)\) are continuously differentiable and \(T\) periodic with respect to \(t\). When \(\varepsilon\) is small enough and \(B(t,x)\) satisfies some superquadratic conditions with respect to \(x\), we prove by critical point theory that the above equation has at least one nontrivial \(T\) periodic solution.

MSC:

37G99 Local and nonlocal bifurcation theory for dynamical systems
34C25 Periodic solutions to ordinary differential equations
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