Periodic and bounded solutions of functional differential equations with small delays (original) (raw)
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The class is singled out of systems described by ordinary differential equations unsolved relative to a derivative, in which a small delay leads to bifurcation of periodic solutions from the equilibrium state. The direct application of the classical results of M.A. Krasnosel'skii to these systems is made difficult in view of the complex character of the dependence on a bifurcation parameter, which is a small delay. The problem on bifurcation of periodic solutions for the stated systems is solved by methods of the theory of rotation of condensing vector fields.
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The class is singled out of systems described by ordinary differential equations unsolved relative to a derivative, in which a small delay leads to bifurcation of periodic solutions from the equilibrium state. The direct application of the classical results of M.A. Krasnosel'skii to these systems is made difficult in view of the complex character of the dependence on a bifurcation parameter, which is a small delay. The problem on bifurcation of periodic solutions for the stated systems is solved by methods of the theory of rotation of condensing vector fields.
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submitted
We investigate criteria for the uniqueness of (mild) periodic solutions to periodic linear functional differential equations with finite delay in Banach spaces. Its arguments are carried out by materializing the theory of seni-Fredholm operators mathrmadotmathrmnmathrmd\mathrm{a}\dot{\mathrm{n}}\mathrm{d}mathrmadotmathrmnmathrmd by using the standard way. In particular, two sufficient conditions ensuring the uniqueness of periodic solutions are obtained : they are independent of each other. [28][29][30][31][32][33][34][35][36]