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Identification of quasiperiodic processes in the vicinity of the resonance

Fischer, Cyril, Náprstek, Jiří (2023)

Programs and Algorithms of Numerical Mathematics

In nonlinear dynamical systems, strong quasiperiodic beating effects appear due to combination of self-excited and forced vibration. The presence of symmetric or asymmetric beatings indicates an exchange of energy between individual degrees of freedom of the model or by multiple close dominant frequencies. This effect is illustrated by the case of the van der Pol equation in the vicinity of resonance. The approximate analysis of these nonlinear effects uses the harmonic balance method and the multiple...

IVPs for singular multi-term fractional differential equations with multiple base points and applications

Yuji Liu, Pinghua Yang (2014)

Applicationes Mathematicae

The purpose of this paper is to study global existence and uniqueness of solutions of initial value problems for nonlinear fractional differential equations. By constructing a special Banach space and employing fixed-point theorems, some sufficient conditions are obtained for the global existence and uniqueness of solutions of this kind of equations involving Caputo fractional derivatives and multiple base points. We apply the results to solve the forced logistic model with multi-term fractional...

Kinetical systems

Ladislav Adamec (1997)

Applications of Mathematics

The aim of the paper is to give some preliminary information concerning a class of nonlinear differential equations often used in physical chemistry and biology. Such systems are often very large and it is well known that where studying properties of such systems difficulties rapidly increase with their dimension. One way how to get over the difficulties is to use special forms of such systems.

Kneser's theorems for strong, weak and pseudo-solutions of ordinary differential equations in Banach spaces

Mieczysław Cichoń, Ireneusz Kubiaczyk (1995)

Annales Polonici Mathematici

We investigate the structure of the set of solutions of the Cauchy problem x’ = f(t,x), x(0) = x₀ in Banach spaces. If f satisfies a compactness condition expressed in terms of measures of weak noncompactness, and f is Pettis-integrable, then the set of pseudo-solutions of this problem is a continuum in C w ( I , E ) , the space of all continuous functions from I to E endowed with the weak topology. Under some additional assumptions these solutions are, in fact, weak solutions or strong Carathéodory solutions,...

Linear distributional differential equations of the second order

Milan Tvrdý (1994)

Mathematica Bohemica

The paper deals with the linear differential equation (0.1) ( p u ' ) ' + q ' u = f ' ' with distributional coefficients and solutions from the space of regulated functions. Our aim is to get the basic existence and uniqueness results for the equation (0.1) and to generalize the known results due to F. V. Atkinson [At], J. Ligeza [Li1]-[Li3], R. Pfaff ([Pf1], [Pf2]), A. B. Mingarelli [Mi] as well as the results from the paper [Pe-Tv] concerning the equation (0.1).

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