An Analysis of Periodic Solutions of Free Vibration in Multiple Degree-of-Freedom Nonlinear Spring-Mass Systems Via Galerkins Procedure : 2nd Report, Oh the Existence of Periodic Solutions Near a Galerkins Approximate Solution

A two degree of freedom oscillator with a colliding component is considered. The aim of the study is to investigate the dynamic behavior of the system when the stiffness obstacle changes to a finite value to an infinite one. Several cases are considered. First, in the case of rigid impact and without external excitation, a family of periodic solutions are found in analytical form. In the case of soft impact, with a finite time duration of the shock, and no external excitation, the existence of periodic solutions, with an arbitrary value of the period, is proved. Periodic motions are also obtained when the system is submitted to harmonic excitation, in both cases of rigid or soft impact. The stability of these periodic motions is investigated for these four cases.

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

Filomat ◽

10.2298/fil1711157a ◽

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.

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

Advanced Nonlinear Studies ◽

10.1515/ans-2020-2075 ◽

2020 ◽

Vol 20 (3) ◽

pp. 725-737 ◽

Cited By ~ 2

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.

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