Existence of Periodic Solutions of Nonlinear Differential Equations

descriptionPublicationkeyboard_double_arrow_right Article 01 Jan 1976Publisher:JSTORJournal:Transactions of the American Mathematical Society, volume 217, page 225 (issn: 0002-9947,

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Authors: Kannan, R.;

doi: 10.2307/1997567 , 10.1090/s0002-9947-1976-0397091-4

Existence of Periodic Solutions of Nonlinear Differential Equations

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Abstract

The nonlinear differential equation x = f ( t , x ( t ) ) x = f(t,x(t)) , f being 2 π 2\pi -periodic in t, is considered for the existence of 2 π 2\pi -periodic solutions. The equation is reduced to an equivalent system of two Hammerstein equations. The case of nonlinear perturbation at resonance is also discussed.

Keywords

Invariant subspaces of linear operators, Periodic solutions to ordinary differential equations

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