A semi-Fredholm principle for periodically forced systems with homogeneous nonlinearities

Lazer, A. C.; McKenna, P. J.

doi:10.1090/S0002-9939-1989-0942635-9

A semi-Fredholm principle for periodically forced systems with homogeneous nonlinearities
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by A. C. Lazer and P. J. McKenna PDF

Proc. Amer. Math. Soc. 106 (1989), 119-125 Request permission

Abstract:

We show that if the potential in a second-order Newtonian system of differential equations is positively homogeneous of degree two and positive semidefinite, and if the unforced system has no nontrivial $T$-periodic solutions $(T > 0)$, then for any continuous $T$-periodic forcing, there is at least one $T$-periodic solution.

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