Periodic Solutions in UMD Spaces for Some Neutral Partial Functional Differential Equations

The aim of this work is to study the existence of a periodic solution for some neutral partial functional differential equations. Our approach is based on the R-boundedness of linear operators Lp-multipliers and UMD-spaces.

OSCILLATION FOR SOLUTIONS OF SYSTEMS OF N-TH ORDER PARTIAL FUNCTIONAL DIFFERENTIAL EQUATIONS

In this paper, some sufficient conditions for the oscillation for solutions to systems of n-th order partial functional differential equations are obtained.

FORCED OSCILLATIONS OF BOUNDARY VALUE PROBLEMS OF HIGHER ORDER FUNCTIONAL PARTIAL DIFFERENTIAL EQUATIONS

In this paper we study the forced oscillations of boundary value problems of a class of higher order functional partial differential equations.The principal tool is an everaging techniqe which enables one to establish oscillation in terms of related functional differential inequallities.

A CLASS OF SECOND ORDER NEUTRAL DIFFERENTIAL INEQUALITIES WITH DISTRIBUTED TYPE DEVIATING ARGUMENTS

In this paper we investigate the properties of the solutions of a class of second order neutral differential inequalities with distributed type deviating arguments . We apply the properties on the inequalities to obtain some new criteria for all solutions of certain neutral hyperbolic partial functions differential equations to be oscillatory.

Neutral Functional Partial Differential Equations Driven by Fractional Brownian Motion with Non-Lipschitz Coefficients

Under a non-Lipschitz condition being considered as a generalized case of Lipschitz condition, the existence and uniqueness of mild solutions to neutral stochas- tic functional differential equations driven by fractional Brownian motion with Hurst parameter 1/2 〈 H 〈 1 are investigated. Some known results are generalized and im- proved.

Hopf Bifurcation of a Gene-Protein Network Module with Reaction Diffusion and Delay Effects

The infinite dimensional partial delay differential equation is set forth and delay difference state feedback control is considered to describe the cell cycle growth in eukaryotic cell cycles. Hopf bifurcation occurs as varying free parameters and time delay continuously and the multi-layer oscillation phenomena of the homogeneous steady state of a simple gene-protein network module is investigated. Normal form is derived based on normal formal analysis technique combined with center manifold theory, which is further to compute the bifurcating direction and the stability of bifurcation periodical solutions underlying Hopf bifurcation. Finally, the numerical simulation oscillation phenomena is in coincidence with the theoretical analysis results.

CAUCHY PROBLEM FOR FRACTIONAL BEAM-LIKE EQUATIONS

In one space-and in one time -dimension a beam-like equation is solved, where the second time derivative is replaced by the α- fractional time derivative, 1 〈 α ≤ 2. The solution is given in closed form in terms of the Mttag-Leffler functions in two parameters.

Oscillation for a Class of Diffusive Hematopoiesis Model with Several Arguments

By considering solution curve＇s or surface＇s composition of the functions of several variables and constructing the suitable lower-upper solution pair for the following special diffusive Hematopoiesis modelunder Neumann boundary condition, sufficient conditions are provided for the oscillation of the positive equilibrium for （0.1）. Moreover, these results extend or complement existing results.