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Periodic solutions of damped differential systems with repulsive singular forces. (English) Zbl 0908.34024
Summary: The author considers the periodic boundary value problem for the singular differential system u '' +(F(u)) ' +G(u)=h(t), with FC 2 ( N ,), GC 1 ( N {0},), and hL 1 ([0,T], N ). The singular potential G(u) is of repulsive type in the sense that G(u)+ as u0. Under Habets-Sanchez’s strong force condition on G(u) at the origin, the existence results, obtained by coincidence degree in this paper, have no restriction on the damping forces (F(u)) ' . Meanwhile, some quadratic growth of the restoring potentials G(u) at infinity is allowed.
MSC:
34C15Nonlinear oscillations, coupled oscillators (ODE)
34C25Periodic solutions of ODE