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Periodic solutions of degenerate differential equations in vector-valued function spaces

Carlos Lizama, Rodrigo Ponce (2011)

Studia Mathematica

Let A and M be closed linear operators defined on a complex Banach space X. Using operator-valued Fourier multiplier theorems, we obtain necessary and sufficient conditions for the existence and uniqueness of periodic solutions to the equation d/dt(Mu(t)) = Au(t) + f(t), in terms of either boundedness or R-boundedness of the modified resolvent operator determined by the equation. Our results are obtained in the scales of periodic Besov and periodic Lebesgue vector-valued spaces.

Periodic solutions of dissipative dynamical systems with singular potential and p-Laplacian

Bing Liu (2002)

Annales Polonici Mathematici

By using the topological degree theory and some analytic methods, we consider the periodic boundary value problem for the singular dissipative dynamical systems with p-Laplacian: ( ϕ p ( x ' ) ) ' + d / d t g r a d F ( x ) + g r a d G ( x ) = e ( t ) , x(0) = x(T), x’(0) = x’(T). Sufficient conditions to guarantee the existence of solutions are obtained under no restriction on the damping forces d/dt gradF(x).

Periodic solutions of evolution problem associated with moving convex sets

Charles Castaing, Manuel D.P. Monteiro Marques (1995)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

This paper is concerned with periodic solutions for perturbations of the sweeping process introduced by J.J. Moreau in 1971. The perturbed equation has the form - D u ∈ N C ( t ) ( u ( t ) ) + f ( t , u ( t ) ) where C is a T-periodic multifunction from [0,T] into the set of nonempty convex weakly compact subsets of a separable Hilbert space H, N C ( t ) ( u ( t ) ) is the normal cone of C(t) at u(t), f:[0,T] × H∪H is a Carathéodory function and Du is the differential measure of the periodic BV solution u. Several existence results of periodic solutions for this...

Periodic solutions of infinite dimensional Riccati Equations

Giuseppe Da Prato (1984)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

Si da un risultato di esistenza di soluzioni periodiche per una equazione di Riccati in dimensione infinita.

Periodic solutions of nonlinear differential systems by the method of averaging

Zhanyong Li, Qihuai Liu, Kelei Zhang (2020)

Applications of Mathematics

In many engineering problems, when studying the existence of periodic solutions to a nonlinear system with a small parameter via the local averaging theorem, it is necessary to verify some properties of the fundamental solution matrix to the corresponding linearized system along the periodic solution of the unperturbed system. But sometimes, it is difficult or it requires a lot of calculations. In this paper, a few simple and effective methods are introduced to investigate the existence of periodic...

Periodic solutions of nth order delay Rayleigh equations

Gen-Qiang Wang, Sui Sun Cheng (2002)

Annales Polonici Mathematici

A priori bounds are established for periodic solutions of an nth order Rayleigh equation with delay. From these bounds, existence theorems for periodic solutions are established by means of Mawhin's continuation theorem.

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