Periodic solutions of perturbed conservative systems

Ward, James R.

doi:10.1090/S0002-9939-1978-0507323-4

Periodic solutions of perturbed conservative systems
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by James R. Ward PDF

Proc. Amer. Math. Soc. 72 (1978), 281-285 Request permission

Abstract:

The existence of $2\pi$-periodic solutions to the system $x'' + \text {grad}\; G(x) = p(t,x)$, p being $2\pi$-periodic in t, is established under conditions at infinity on the Hessian matrix of G. The condition used is weaker than earlier known conditions of a similar nature.

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Fixed point theorems