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SECOND ORDER CORRECTIONS TO MEAN FIELD EVOLUTION FOR WEAKLY INTERACTING BOSONS, I
SECOND ORDER equation
2015/10/15
Inspired by the works of Rodnianski and Schlein [31]
and Wu [34, 35], we derive a new nonlinear Schr¨odinger equation
that describes a second-order correction to the usual tensor product (mean-ʂ...
Hopf bifurcation formula for first order differential-delay equations
Hopf bifurcation Differential delay equation DDE Retarded functional differential equation RFDE
2015/8/27
This work presents an explicit formula for determining the radius of a limit cycle which is born in a Hopf bifurcation in a class of first order constant coefficient differential-delay equations. The ...
Anisotropic interactions in a first-order aggregation model:a proof of concept
Anisotropy visual perception aggregation models implicit equations regularization relaxation time uniqueness criteria singular perturbation
2015/7/14
We extend a well-studied ODE model for collective behaviour by considering anisotropic interactions among individuals. Anisotropy is modeled by limited sensorial perception of individuals, that depend...
Point classification of the second order ODE's by Ruslan Sharipov and its application to Painleve equations
Point classification the second order ODE's Ruslan Sharipov Painleve equations
2012/4/17
This is an review on the point classification of second order ODE's by Ruslan Sharipov. His works were published in 1997-1998 at the Electronic Archive at LANL and undeservedly forgotten. Last chapter...
Semipositone Problems of Second Order Ordinary Differential Equations
Positive solution Semipositone boundary value problem Ordinary differential equation
2011/10/12
The paper is concerned with the semipositone boundary value problems of second-order ordinary differential equations. Applying a fixed point theorem in cones, an existence result of at least one posit...
Existence of n Positive Solutions for Some Fourth-order Boundary Value Problems
nonlinear fourth-order boundary value problems positive solution existence multiplicity fixed point theorem on cone Leray-Schauder continuous principle
2011/10/12
The authors apply Leray-Schauder continuous principle theorem and Krasnosel’skii fixed point theorem of cone expansion-compression type to a class of nonlinear fourth-order two-point boundary value pr...
Existence of n Positive Solutions for Some Fourth-order Boundary Value Problems
nonlinear fourth-order boundary value problems positive solution existence multiplicity fixed point theorem on cone Leray-Schauder continuous principle
2011/10/12
The authors apply Leray-Schauder continuous principle theorem and Krasnosel’skii fixed point theorem of cone expansion-compression type to a class of nonlinear fourth-order two-point boundary value pr...
Oscillation and non-oscillation of second-order half-linear differential equations
Half-linear differential equations oscillation non-oscillation
2011/10/12
In this paper, we consider the oscillation and non-oscillation of second order half-linear differential equation. By using some new technique, we establish new oscillation and non-oscillation criteria...
Equivalence classes of the second order ODEs with the constant Cartan invariant
Invariant Equivalence Problem Ordinary Differential Equation Point transformation Painleve equation Emden equation
2011/7/6
Second order ordinary differential equations that possesses the constant invariant are investigated. Four basic types of these equations were found. For every type the complete list of nonequivalent e...
Nonlinear Stabilization under Sampled and Delayed Measurements, and with Inputs Subject to Delay and Zero-Order Hold
feedback stabilization time-delay systems sampled-data systems nonlinear control
2011/1/20
Sampling arises simultaneously with input and output delays in networked control systems. When the delay is left uncompensated, the sampling period is generally required to be sufficiently small, the ...
Positive periodic solutions of singular systems of first order ordinary differential equations
Periodic solutions singular system Krasnoselskii fixed point
2010/12/10
The existence and multiplicity of positive periodic solutions for first non-autonomous singular systems are established with superlinearity or sublinearity assumptions atinfinity for an appropriately ...
A Filippov Type Existence Theorem for a Class of Second-Order Differential Inclusions
Differential inclusion Measurable selection Solution set
2010/1/25
We prove a Filippov-Gronwall type inequality for solutions of a nonconvex second-order differential inclusion of Sturm-Liouville type.
Multiple Positive Solutions for Nonlinear Third-Order Boundary Value Problems in Banach Spaces
Positive solutions boundary value problem Banach spaces fixed point index
2010/2/25
This paper deals with the positive solutions of nonlinear boundary value problems in Banach spaces. By using fixed point index theory, some sufficient conditions for the existence of at least one or t...
In this paper, we develop a new teclinique called multiplicative extrapolation method which is used to construct higher order schemes for ordinary dtherential equations. We call it a new method becaus...
Oscillation of nonlinear neutral delay differential equations of second-order with positive and negative coefficients
Delay differential equations neutral nonlinear oscillation second-order
2010/2/25
Some oscillation criteria for the following second-order neutral differential equation [x(t)\pm r(t) f( x(t-g))]''+p(t) g(x(t-a)) -q(t) g(x(t-b )) = s(t) where t\geq t0, g,a,b \in R+ with a \geq b, r ...