On the existence of periodic solutions to higher dimensional periodic system with delay

Ｃｏｎｓｉｄｅｒｉｎｇｔｈｅｈｉｇｈｅｒｄｉｍｅｎｓｉｏｎａｌｐｅｒｉｏｄｉｃｓｙｓｔｅｍｓｗｉｔｈｄｅｌａｙｏｆｔｈｅｆｏｒｍｘ′（ｔ）＝Ａ（ｔ,ｘ（ｔ））ｘ（ｔ）＋ｆ（ｔ,ｘ（ｔ－τ））,（１）ｘ′（ｔ）＝ｇｒａｄＧ（ｘ（ｔ））＋ｆ（ｔ,ｘ（ｔ－...     

Linearized oscillations for autonomous delay differential equations

ＩｎｔｒｏｄｕｃｔｉｏｎＣｏｎｓｉｄｅｒｔｈｅｎｏｎｌｉｎｅａｒａｕｔｏｎｏｍｏｕｓｄｅｌａｙｄｉｆｆｅｒｅｎｔｉａｌｅｑｕａｔｉｏｎｘ′(ｔ) ∑ｍｉ=1ｐｉｆｉ(ｘ(ｔ-τｉ) ) =0 (1 )ａｎｄｔｈｅｌｉｎｅａｒｅｑｕａｔｉｏｎｘ′(ｔ) ∑ｍｉ=1ｐｉｘ(ｔ-τｉ) =0 ,(2 )ｗｈｅｒｅ ,ｐｉ ∈ (0 ,∞ ) ,τｉ ∈ [0 ,∞ )ａｎｄｆｉ ∈Ｃ(Ｒ ,Ｒ)ｆｏｒｉ =1 ,… ,ｍ .ＩｎＲｅｆ.[1 ] ,ｔｈｅｌｉｎｅａｒｉｚｅｄｏｓｃｉｌｌａｔｉｏｎｓｏｆＥｑ .(1 )ｗａｓｓｔｕｄｉｅｄａｎｄｉｔｗａｓｐｒｏｖｅｄｔｈａｔｉｆｔ…     

Existence and Multiplicity of Positive Solutions for a Fourth-Order P-Laplace Equations

Ｉｎｔｒｏｄｕｃｔｉｏｎｐ＿Ｌａｐｌａｃｅｅｑｕａｔｉｏｎｓａｒｉｓｅｉｎａｖａｒｉｅｔｙｏｆｉｎｔｅｒｅｓｔｉｎｇａｐｐｌｉｃａｔｉｏｎｓ,ｔｈｅｙａｐｐｅａｒａｓｍｏｄｅｌｓｏｆｇａｓｄｉｆｆｕｓｉｏｎｔｈｒｏｕｇｈｐｏｒｏｕｓｍｅｄｉａ,ａｌｓｏｉｎｔｈｅｔｈｅｏｒｙｏｆｔｈｅｒｍａｌｓｅｌｆ＿ｉｇｎｉｔｉｏｎｏｆａｃｈｅｍｉｃａｌｌｙａｃｔｉｖｅｍｉｘｔｕｒｅｏｆｇａｓｅｓ(ｓｅｅ [1 ]ａｎｄｉｔｓｒｅｆｅｒｅｎｃｅｓ) ,ｒｅｃｅｎｔｌｙ ,ＷＡＮＧＪｕｎ＿ｙｕ (Ｒｅｆ.[1 ] )ｓｔｕｄｉｅｄｔｈ…     

Higher Order Approximation of the Period-energy Function for Single Degree of Freedom Hamiltonian Systems

In 1985 Franz Rothe [J. Reine Angew Math. 355 (1985) 129–138] found, by means of the thermodynamical equilibrium theory, an asymptotic estimate of the period of solutions of ordinary differential equations originated by predator–prey Volterra–Lotka model. We extend some of the Rothe's ideas to more general systems:

On Asymptotic Properties of Continuously Differentiable Solutions of Quasilinear Functional Differential Equations

We establish new properties of C ¹ [τ(1), + ∞)-solutions of the quasilinear functional differential equation

Global solvability of one degenerate semilinear differential operator equation

We consider the Cauchy problem for the abstract semilinear differential equation where A and B are linear closed, generally speaking, degenerate operators acting from a Banach space X into a Banach space Y and f(t, u) is a continuously differentiable function. We assume that the resolvent (A + B)^–1 has a pole of at most second order at the point = 0. Global conditions for the existence and uniqueness of a solution of the Cauchy problem are obtained. The results are applied to a nonlinear degenerate initial boundary-value problem with partial derivatives and to a system of differential-algebraic equations of a nonlinear electric circuit.Translated from Neliniini Kolyvannya, Vol. 7, No. 3, pp. 414–429, July–September, 2004.     

Solvability of Degenerate Semilinear Parabolic Functional Differential Equations

We obtain local and global theorems on the existence and uniqueness of a solution of the semilinear functional differential equation in a Banach space with a parabolic pencil of operators A + B, where the operator A can be noninvertible. Abstract results are applied to partial functional differential equations.     

The Extinction Behavior of the Solutions for a Class of Reaction-Diffusion Equations

1　ＩｎｔｒｏｄｕｃｔｉｏｎａｎｄＬｅｍｍａｓＴｈｅｒｅａｒｅｍａｎｙｒｅｓｕｌｔｓａｂｏｕｔｅｘｉｓｔｅｎｃｅ (ｇｌｏｂａｌｏｒｌｏｃａｌ)ａｎｄａｓｙｍｐｔｏｔｉｃｂｅｈａｖｉｏｒｏｆｓｏｌｕｔｉｏｎｓｆｏｒｒｅａｃｔｉｏｎ＿ｄｉｆｆｕｓｉｏｎｅｑｕａｔｉｏｎｓ[1- 9].Ｂｙｔｈｅａｉｄｓｏｆｒｅｓｕｌｔｓ[2 ,3]ｏｆｅｑｕａｔｉｏｎ ｕ/ ｔ=Δｕ-λ｜ｕ｜γ- 1ｕｗｉｔｈｉｎｉｔｉａｌ＿ｂｏｕｎｄａｒｙｖａｌｕｅｓ,ｐａｐｅｒ [4 ]ｓｔｕｄｉｅｄｔｈｅｐｒｏｂｌｅｍｏｆ ｕ/ ｔ=Δｕ-λ｜ｅβｔｕ｜γ- …     

Almost Periodicity in an Ecological Model with <Emphasis Type="Italic">M</Emphasis>-Predators and <Emphasis Type="Italic">N</Emphasis>-Preys by “Pure-Delay Typ” System

By using comparison theorem and constructing suitable Lyapunov functional, we study the following periodic Lotka–Volterra model with M-predators and N-preys by pure-delay type

Asymptotic and oscillation of the solutions for a class of the first order neutral differential equations

ＩｎｔｒｏｄｕｃｔｉｏｎＯｗｉｎｇｔｏｔｈｅｅｘｔｅｎｓｉｖｅａｐｐｌｉｃａｔｉｏｎｏｆｎｅｕｔｒａｌｅｑｕａｔｉｏｎｓ,ｍｏｒｅａｎｄｍｏｒｅｓｔｕｄｉｅｓｈａｖｅｂｅｎｍａｄｅｏｎｔｈｅｂｅｈａｖｉｏｒｏｆｔｈｅｓｏｌｕｔｉｏｎｓ［１,２］．Ｆｏ...     

Stability of a class of neural network models with delay

ＩｎｔｒｏｄｕｃｔｉｏｎＲｅｃｅｎｔｌｙ,ｔｈｅｏｒｅｔｉｃａｌａｎｄａｐｌｉｅｄｓｔｕｄｉｅｓｏｆｎｅｕｒａｌｎｅｔｗｏｒｋｍｏｄｅｌｈａｖｅｂｅｎｔｈｅｎｅｗｆｏｃｕｓｏｆｓｔｕｄｉｅｓｉｎｔｈｅｗｏｒｌｄ．Ｉｔｉｓｗｅｌ＿ｋｎｏｗｎｔｈａｔｑｕ...     

Positive periodic solution of a neutral predator-prey system

ＩｎｔｒｏｄｕｃｔｉｏｎＡｔｐｒｅｓｅｎｔ,ｔｈｅｒｅａｒｅｏｎｌｙａｆｅｗｐａｐｅｒｓ［１～３］ｈａｖｉｎｇｂｅｎｐｕｂｌｉｓｈｅｄｏｎｔｈｅｇｌｏｂａｌｅｘｉｓｔｅｎｃｅｏｆｐｅｒｉｏｄｉｃｓｏｌｕｔｉｏｎｓｆｏｒｎｅｕｔｒａｌｄｅｌａｙｐｏｐｕ...     

A technique for evaluation of three-dimensional behavior in turbulent boundary layers using computer augmented hydrogen bubble-wire flow visualization

A system is described which allows the recreation of the three-dimensional motion and deformation of a single hydrogen bubble time-line in time and space. By digitally interfacing dualview video sequences of a bubble time-line with a computer-aided display system, the Lagrangian motion of the bubble-line can be displayed in any viewing perspective desired. The u and v velocity history of the bubble-line can be rapidly established and displayed for any spanwise location on the recreated pattern. The application of the system to the study of turbulent boundary layer structure in the near-wall region is demonstrated.List of Symbols Reynolds number based on momentum thickness u /v - t⁺ nondimensional time - u shear velocity - u local streamwise velocity, x-direction - u ⁺ nondimensional streamwise velocity - v local normal velocity, -direction - x ⁺ nondimensional coordinate in streamwise direction - ⁺ nondimensional coordinate normal to wall - ₊ ^wire wire nondimensional location of hydrogen bubble-wire normal to wall - z ⁺ nondimensional spanwise coordinate - momentum thickness - v kinematic viscosity - _W wall shear stress     

Numerical stability analysis of numerical methods for volterra integral equations with delay argument

The present paper deals with the stability properties of numerical methods for Volterra integral equations with delay argument. We assess the numerical stability of numerical methods with respect to the following test equations (0.1a) $$y\left( t \right) = \psi \left( 0 \right) + \int_0^t {\left( {py\left( s \right) + q\left( {s - \tau } \right)} \right)ds (0 \leqslant t \leqslant X)}$$ (0.1b) $$y\left( t \right) = \psi \left( t \right) \left( {t \in [ - \tau ,0)} \right)$$ where τ is a positive constant, and P and q are complex valued. We investigate the stability properties of reducible quadrature methods and θ-methods in the case of the above test equations     

On the Denseness of the Set of Unsolvable Cauchy Problems in the Set of All Cauchy Problems in the Case of an Infinite-Dimensional Banach Space

We prove the following statement: Theorem 1. Let E and be an arbitrary infinite-dimensional Banach space and a continuous mapping, respectively. Then, for every and > 0, there exists a continuous mapping such that

Oscillation Types and Bifurcations of a Nonlinear Second-Order Differential-Difference Equation

This paper considers the second-order differential difference equation

The flow regime in the turbulent near wake of a hemisphere

The work presented is a wind tunnel study of the near wake region behind a hemisphere immersed in three different turbulent boundary layers. In particular, the effect of different boundary layer profiles on the generation and distribution of near wake vorticity and on the mean recirculation region is examined. Visualization of the flow around a hemisphere has been undertaken, using models in a water channel, in order to obtain qualitative information concerning the wake structure.List of symbols C _p pressure coefficient, - D diameter of hemisphere - n vortex shedding frequency - p pressure on model surface - p ₀ static pressure - Re Reynolds number, - St Strouhal number, - U, V, W local mean velocity components - mean freestream velocity inX direction - U ^* shear velocity, - u, v, w velocity fluctuations inX, Y andZ directions - X Cartesian coordinate in longitudinal direction - Y Cartesian coordinate in lateral direction - Z Cartesian coordinate in direction perpendicular to the wall - it* boundary layer displacement thickness, - diameter of model surface roughness - elevation angleI - O boundary layer momentum thickness, - _w wall shearing stress - dynamic viscosity of fluid - density of fluid - streamfunction - _x longitudinal component of vorticity, - _y lateral component of vorticity, - _z vertical component of vorticity, This paper was presented at the Ninth symposium on turbulence, University of Missouri-Rolla, October 1–3, 1984     

Analysis of thermally activated formation and breakdown of Kear-Wilsdorf barriers in Ni<Subscript>3</Subscript>Ge single crystals of various orientations

The orientation dependence of the yield stress in Ni₃Ge single crystals has been examined both theoretically and experimentally. The positive temperature dependence of the yield stress in the low temperature region is attributed to formation of Kear-Wilsdorf barriers. The forces driving the formation and breakdown of barriers are calculated within the framework of the Hirsch scheme. A distinctive feature of the model proposed is that the barrier is considered on the screw component of the a/2[ 01](111) superdislocation in the primary octahedral plane. The major role in barrier formation belongs to anisotropy of elastic moduli, energy of antiphase boundaries in the octahedral plane, shear stresses in the cubic and octahedral planes, and friction-induced stress in the cubic plane. A comparison of predicted values of the driving force of barrier formation and breakdown with experimental values reveals their good agreement. An analysis of the orientation dependence of the driving force of barrier formation in the temperature range T = 77–293 K shows that the dependence (T) has an extremum for crystals deformed along the [ 39] crystallographic direction, which is confirmed experimentally.Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 46, No. 1, pp. 116–125, January–February, 2005.     

Classical solutions of hyperbolic initial boundary-value problems with state-dependent delays

We consider the initial boundary-value problem for a system of quasilinear partial functional differential equations of the first order

Normal hyperbolicity of center manifolds and Saint-Venant's principle

The concept of normal hyperbolicity of center manifolds is generalized to infinite-dimensional differential equations, in particular, to elliptic problems in cylindrical domains. It is shown that all solutions u staying close to the center manifold for t (–l,l) satisfy an estimate of the form where C and are independent of l, and is a solution on the center manifold. These results are applied to Saint-Venant's principle for the static deformation of nonlinearly elastic prismatic bodies. The use of the center manifold permits the effective treatment of the general case of non-zero resultant forces and moments acting on each cross-section.