This paper presents criteria for the existence and uniqueness of solutions to five-point boundary value problems associated with third order differential equations by using matching technique. ’Liapunov-like’ functions are used as a tool to establish existence and uniqueness of solutions by matching two three-point boundary value problems. AMS Mathematics Subject Classification (2000): 34B10, 3...

The existence and comparison theorem of solutions is first established for the quasimonotone delayed reaction-diffusion equations on R by appealing to the theory of abstract functional differential equations. The global asymptotic stability, Liapunov stability and uniqueness of traveling wave solutions are then proved by the elementary superand sub-solution comparison and squeezing methods. Sup...

The essential decorrelation rate of a hyperbolic dynamical system is the decay rate of time-correlations one expects to see stably for typical observables once resonances are projected out. We define and illustrate these notions and study the conjecture that for observables in C1, the essential decorrelation rate is never faster than what is dictated by the smallest unstable Liapunov multiplier.

in this paper, we explore a nonlinear mathematical model to study the spread of asthma due to inhaled pollutants from industry as well as tobacco smoke from smokers in a variable size population. the model is analyzed using stability theory of differential equations and computer simulation. it is shown that with an increase in the level of air pollutants concentration, the asthmatic (diseased) ...

The Liapunov Razumikhin technique is applied to obtain the uniform asymptotic stability for linear integrodifferential equations in Hilbert spaces, x′(t) = A [ x(t) + ∫ t # F (t− s)x(s)ds ] , t ≥ t0 ≥ 0, (# = 0 or −∞), which occur in viscoelasticity and in heat conduction for materials with memory.

Integral Hamzeh Agahi,1,† Adel Mohammadpour,1,∗ Radko Mesiar,2,3,‡ S. Mansour Vaezpour1,§ Department of Statistics, Faculty of Mathematics and Computer Science, Amirkabir University of Technology (Tehran Polytechnic), Tehran 15914, Iran Department of Mathematics and Descriptive Geometry, Faculty of Civil Engineering, Slovak University of Technology, SK-81368 Bratislava, Slovakia Institute of In...

We describe a method to investigate the mode shapes in turbulent pipe flow at a given wavenumber pair that are most responsive to harmonic forcing in the sense that the they correspond to the largest singular value in a Schmidt decomposition of the linear NavierStokes operator using the turbulent mean profile as the base flow. The ideas follow logically from the work of Sharma & McKeon (2009), ...

Gabor Matthäus, Stefan Nolte, Rico Hohmuth, Martin Voitsch, Wolfgang Richter, Boris Pradarutti, Stefan Riehemann, Gunther Notni, and Andreas Tünnermann Institute of Applied Physics, Friedrich-Schiller-University Jena, Max-Wien-Platz 1, Jena D-07743, Germany BATOP GmbH, Wildenbruchstrasse 15, Jena D-07745, Germany Fraunhofer Institute for Applied Optics and Precision Engineering, Albert-Einstein...