Rotating periodic integrable solutions for second-order differential systems with nonresonance condition

<abstract><p>In this paper, we investigate the existence and uniqueness of solutions for nonlinear quadratic iterative equations in the sense of the Caputo fractional derivative with different boundary conditions. Under a one-sided-Lipschitz condition on the nonlinear term, the existence and uniqueness of a solution for the boundary value problems of Caputo fractional iterative equations with arbitrary order is demonstrated by applying the Leray-Schauder fixed point theorem and topological degree theory, where the solution for the case of fractional order greater than 1 is monotonic. Then, the existence and uniqueness of a solution for the period and integral boundary value problems of Caputo fractional quadratic iterative equations in $ R^N $ are also demonstrated. Furthermore, the well posedness of the control problem of a nonlinear iteration system with a disturbance is established by applying set-valued theory, and the existence of solutions for a neural network iterative system is guaranteed. As an application, an example is provided at the end.</p></abstract>

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Rotating periodic integrable solutions for second-order differential systems with nonresonance condition

Cited by 3 publications

References 12 publications

Rotating periodic solutions in complete degeneracy

Rotating periodic solutions in complete degeneracy

Hopf bifurcation theorem of rotating periodic solutions in a class of anti-synchronous systems

Existence of solutions for Caputo fractional iterative equations under several boundary value conditions

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