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Subharmonic solutions of a nonconvex noncoercive Hamiltonian system. (English) Zbl 1108.34034

The existence of subharmonic solutions of the Hamiltonian system
\[ J\dot{x} +u^{*} \triangledown G(t,u(x))=e(t) \tag{1} \]
is considered, where \(u\) is a linear map, \(G(t,y)\) is a continuous function, \(T\)-periodic in the first variable with \(T>0\), \(e(t)\) is a continuous function and \(J\) is the standard symplectic matrix. Several theorems concerning existence of \(T\)-periodic solutions and \(kT\)-periodic solutions of system (1) are proved.

MSC:

34C25 Periodic solutions to ordinary differential equations
37J45 Periodic, homoclinic and heteroclinic orbits; variational methods, degree-theoretic methods (MSC2010)
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References:

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