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Periodic second order superlinear Hamiltonian systems. (English) Zbl 1327.34073

Using linking and sandwich methods of critical point theory, the author proves several sufficient conditions for the existence of \(T\)-periodic solutions of second order systems of the form \[ - x''{} = B(t)x + \nabla_x V(t,x) \] when \(V(t,x) \geq (\lambda_{l-1}/2)|x|^2\) for some eigenvalue \(\lambda_{l-1}\) of the \(T\)-periodic problem for the linear part \(-x''{} _ B(t)x\), \(V(t,x)\) is superquadratic in \(x\) at infinity and \(V\) satisfies other conditions.

MSC:

34C25 Periodic solutions to ordinary differential equations
58E05 Abstract critical point theory (Morse theory, Lyusternik-Shnirel’man theory, etc.) in infinite-dimensional spaces
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