A note on the existence of periodic solutions of a differential system

1988 ◽  
pp. 94-99
Author(s):  
Hsin Chu
Keyword(s):  
Periodic Solutions ◽  
Differential System ◽  
Existence Of Periodic Solutions

scholarly journals On the Generalized Reflective Function of the Three-Degree Polynomial Differential System

2019 ◽  
Vol 2019 ◽  
pp. 1-6
Author(s):  
Jian Zhou ◽  
Shiyin Zhao
Keyword(s):  
Periodic Solutions ◽  
Differential System ◽  
Reflective Function ◽  
Degree Polynomial ◽  
Differential Systems ◽  
Polynomial Differential Systems ◽  
Polynomial Differential System ◽  
Existence Of Periodic Solutions

The structure of the generalized reflective function of three-degree polynomial differential systems is considered in this paper. The generated results are used for discussing the existence of periodic solutions of these systems.

scholarly journals Nontrivial Periodic Solutions of an -Dimensional Differential System and Its Application

2013 ◽  
Vol 2013 ◽  
pp. 1-9
Author(s):  
F. B. Gao
Keyword(s):  
Periodic Solutions ◽  
Thin Plate ◽  
Differential System ◽  
Nonlinear Term ◽  
Periodic Motions ◽  
Rectangular Thin Plate ◽  
Simply Supported ◽  
Nontrivial Periodic Solutions ◽  
Existence Of Periodic Solutions ◽  
Plate System

Two criteria are constructed to guarantee the existence of periodic solutions for a second-order -dimensional differential system by using continuation theorem. It is noticed that the criteria established are found to be associated with the system’s damping coefficient, natural frequency, parametrical excitation, and the coefficient of the nonlinear term. Based on the criteria obtained, we investigate the periodic motions of the simply supported at the four-edge rectangular thin plate system subjected to the parametrical excitation. The effectiveness of the criteria is validated by corresponding numerical simulation. It is found that the existent range of periodic solutions for the thin plate system increases along with the increase of the ratio of the modulus of nonlinear term’s coefficient and parametric excitation term, which generalize and improve the corresponding achievements given in the known literature.

scholarly journals Periodic Solutions of Some Polynomial Differential Systems in Dimension 3 via Averaging Theory

2015 ◽  
Vol 2015 ◽  
pp. 1-10 ◽  
Author(s):  
Amar Makhlouf ◽  
Lilia Bousbiat
Keyword(s):  
Small Parameter ◽  
Real Number ◽  
Periodic Solutions ◽  
Differential System ◽  
Sufficient Conditions ◽  
Periodic Functions ◽  
Third Order ◽  
Differential Systems ◽  
Polynomial Differential Systems ◽  
Existence Of Periodic Solutions

We provide sufficient conditions for the existence of periodic solutions of the polynomial third order differential systemx.=-y+εP(x,y,z)+h1(t),  y.=x+εQ(x,y,z)+h2(t),  and  z.=az+εR(x,y,z)+h3(t), whereP,Q, andRare polynomials in the variablesx,y, andzof degreen,  hi(t)=hi(t+2π)withi=1,2,3being periodic functions,ais a real number, andεis a small parameter.

A new Ф-generalized quasi metric space with some fixed point results and applications

Filomat ◽  
2017 ◽  
Vol 31 (11) ◽  
pp. 3157-3172
Author(s):  
Mujahid Abbas ◽  
Bahru Leyew ◽  
Safeer Khan
Keyword(s):  
Fixed Point ◽  
Differential Equations ◽  
Fixed Points ◽  
Periodic Solutions ◽  
Metric Space ◽  
Delay Differential Equations ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Existence Of Periodic Solutions ◽  
Delay Differential

In this paper, the concept of a new ?-generalized quasi metric space is introduced. A number of well-known quasi metric spaces are retrieved from ?-generalized quasi metric space. Some general fixed point theorems in a ?-generalized quasi metric spaces are proved, which generalize, modify and unify some existing fixed point theorems in the literature. We also give applications of our results to obtain fixed points for contraction mappings in the domain of words and to prove the existence of periodic solutions of delay differential equations.

Periodic Solutions of Non-autonomous Allen–Cahn Equations Involving Fractional Laplacian

2020 ◽  
Vol 20 (3) ◽  
pp. 725-737 ◽  
Author(s):  
Zhenping Feng ◽  
Zhuoran Du
Keyword(s):  
Variational Methods ◽  
Periodic Solutions ◽  
Smooth Function ◽  
Fractional Laplacian ◽  
Type Inequality ◽  
Energy Functional ◽  
Large Integer ◽  
Existence Of Periodic Solutions ◽  
Double Well Potential

AbstractWe consider periodic solutions of the following problem associated with the fractional Laplacian: {(-\partial_{xx})^{s}u(x)+\partial_{u}F(x,u(x))=0} in {\mathbb{R}}. The smooth function {F(x,u)} is periodic about x and is a double-well potential with respect to u with wells at {+1} and -1 for any {x\in\mathbb{R}}. We prove the existence of periodic solutions whose periods are large integer multiples of the period of F about the variable x by using variational methods. An estimate of the energy functional, Hamiltonian identity and Modica-type inequality for periodic solutions are also established.

scholarly journals On the equivalence of three-dimensional differential systems

2020 ◽  
Vol 18 (1) ◽  
pp. 1164-1172
Author(s):  
Jian Zhou ◽  
Shiyin Zhao
Keyword(s):  
Periodic Solutions ◽  
Differential System ◽  
Necessary Conditions ◽  
Three Dimensional ◽  
Sufficient Conditions ◽  
Periodic Systems ◽  
Structural Form ◽  
Differential Systems

Abstract In this paper, firstly, we study the structural form of reflective integral for a given system. Then the sufficient conditions are obtained to ensure there exists the reflective integral with these structured form for such system. Secondly, we discuss the necessary conditions for the equivalence of such systems and a general three-dimensional differential system. And then, we apply the obtained results to the study of the behavior of their periodic solutions when such systems are periodic systems in t.

Existence of periodic solutions for a class of nonlinear problems

1983 ◽  
Vol 7 (8) ◽  
pp. 873-879 ◽  
Author(s):  
Philip Korman
Keyword(s):  
Periodic Solutions ◽  
Nonlinear Problems ◽  
Existence Of Periodic Solutions
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