Kong, Fanchao Liang, Feng Nieto, Juan J.
Published in
Qualitative Theory of Dynamical Systems

This paper mainly aims to investigate the positive periodic solutions for coupled singular Rayleigh systems. In order to establish the coupled structure, the basic framework of graph theory is employed. By means of Lyapunov method, inequality techniques and a classical consequence of Mawhin’s continuation theorem, some sufficient criterion for the ...

Hirsch, MW Turiel, FJ

© 2019, Springer Nature B.V. Unless another thing is stated one works in the C∞ category and manifolds have empty boundary. Let X and Y be vector fields on a manifold M. We say that Y tracks X if [Y, X] = fX for some continuous function f: M→ R. A subset K of the zero set Z(X) is an essential block for X if it is non-empty, compact, open in Z(X) an...

Maleval, Francis

A mirror built here, by virtue of an iterative process, a geometry from a conceptual object. This dynamic, served by the Noether’s theorem, generates the universal constants.

Haidar, Ihab Barbot, Jean-Pierre Rapaport, Alain

We consider the observation problem for a particular class of bidimensional systems with scalar output which requires the construction of an embedding in higher dimension. We propose a new approach that does not require any coordinates transformation. This approach is based on the design of parallel estimators in the same dimension than the origina...

Margheri, Alessandro Misquero, Mauricio
Published in
Celestial Mechanics and Dynamical Astronomy

In this work, we consider the Kepler problem with a family of singular dissipations of the form -k|x|βx˙,k>0,β>0.\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$-\frac{...

Challis, John H.
Published in
BMC Biomedical Engineering

BackgroundThe three-dimensional description of rigid body kinematics is a key step in many studies in biomechanics. There are several options for describing rigid body orientation including Cardan angles, Euler angles, and quaternions; the utility of quaternions will be reviewed and elaborated.Main body of abstractThe orientation of a rigid body or...

Shankar, Karthik H.
Published in
General Relativity and Gravitation

The question of whether the universe is eternal or if it had a singular moment of creation is deeply intriguing. Although different versions of steady state and oscillatory models of eternal universe have been envisaged, empirical evidence suggests a singular moment of creation at the big bang. Here we analyze the oscillatory solutions for the univ...

Wang, Yongqing
Published in
Advances in Difference Equations

In this paper, we consider a Riemann–Liouville type two-term fractional differential equation boundary value problem. Some positive properties of the Green’s function are deduced by using techniques of analysis. As application, we obtain the existence and multiplicity of positive solutions for a fractional boundary value problem under conditions th...

Deng, Yanxia Ibrahim, Slim
Published in
Qualitative Theory of Dynamical Systems

We use the idea of ground states and excited states in nonlinear dispersive equations (e.g. Klein-Gordon and Schrödinger equations) to characterize solutions in the N-body problem with strong force under some energy constraints. Indeed, relative equilibria of the N-body problem play a similar role as solitons in PDE. We introduce the ground state a...

Egorov, Vladimir V.
Published in
Heliyon

Atomic physics; Condensed matter physics; Electromagnetism; Molecular physics; Optics; Quantum mechanics; Physics methods; Theoretical physics; Quantum mechanics; Molecular quantum transitions; Singularity; Dozy chaos; Quantum-classical mechanics; Electron transfer; Condensed matter; Applications