Criteria of general weak type inequalities for integral transforms with positive kernels

Necessary and sufficient conditions are derived in order that an inequality of the form

Existence and uniqueness of limit cycles on a cubic kolmogorov differential system in the Predator-Prey relation

In this paper, we analyse qualitatively a cubic Kolmogorov system: which is one of the mathematical models in ecology describing the interaction between Predator-Prey of two populations; and give the conditions of nonexistence, existence and uniqueness of limit cycles for three different cases.Fulfilled during engagement in advanced studies at the Institute of Mathematics, Academia Sinica.     

具强迫力的奇数阶中立型微分方程的振动性

Abstract. In this paper, the forced odd order neutral differential equations of the form are con-sidered     

On a Singular Two-Point Boundary Value Problem for the Nonlinear mth-Order Differential Equation with Deviating Arguments

Sufficient conditions of solvability and unique solvability of the boundary value problem are established, where are measurable functions and the vector function is measurable in the first and continuous in the last kmn arguments; moreover, this function may have nonintegrable singularities with respect to the first argument.     

Analytic solutions of differential-functional equations

We consider the general differential-functional equations

Sums of Five, Seven and Nine Squares

Let r _k(n) denote the number of representations of an integer n as a sum of k squares. We prove that

The critical exponent for a weakly coupled system of the generalized Fujita type reaction-diffusion equations

We study nonnegative solutions of the initial value problem for a weakly coupled system

On the asymptotic stability ofθ-methods for delay differential equations

Stability regions of -methods for the linear delay differential test equations

An asymptotic theorem for a class of nonlinear neutral differential equations

The neutral differential equation is considered under the following conditions: n 2, > 0, = ±1, F(t, u) is nonnegative on [t ₀, ) × (0, ) and is nondecreasing in u (0, infin;), and lim g(t) = as t . It is shown that equation (1.1) has a solution x(t) such that 0}}{\text{.}} \hfill \\ \end{gathered} $$ " align="middle" border="0"> Here, k is an integer with 0 k n–1. To prove the existence of a solution x(t) satisfying (1.2), the Schauder-Tychonoff fixed point theorem is used.     

Arithmetical Functions of the Form f([g(n)])

Two results on composed functions are proven. First we give conditions on and so that the mean behaves like , if , including the examples

Zero–One Law for some Brownian Functionals

We prove that for a>0, (B _t) one-dimensional standard Brownian motion and ₀=inf{t>0 : B _t=0} the following zero–one law is valid

Brownian motion with negative drift and convex level sets in space-time

Suppose a, b, and are reals witha<b and consider the following diffusion equation

Existence,uniqueness and convergence as vanishing viscosity for a reaction-diffusion-convection system

A simple qualitative model of dynamic combustion

Arithmetic properties of the values of a set of functions satisfying a system of differential equations

General results were presented in [2] and [3] concerning arithmetic properties of the values at algebraic points of a class of analytic functions satisfying linear differential equations. In the present note we consider the application of these results to the set of functions $$\begin{gathered} ^f (\alpha _k z) = \sum\nolimits_{n = 0}^\infty {\frac{{ \mu (\mu + 1)... (\mu + n - 1) }}{{\lambda (\lambda + 1)... (\lambda + n - 1)}}} (\alpha _k z)^n (k = 1,2,...,m,) \hfill \\ \lambda \ne 0, - 1, - 2,...), \hfill \\ \end{gathered}$$ where α₁, ..., α_m are algebraic numbers; λ and μ are rational numbers; and the functions satisfy a system of linear differential equations.     

A survey and some new results on the existence of solutions of IPBVPS for first order functional differential equations

This paper deals with the periodic boundary value problem for nonlinear impulsive functional differential equation

Boundary value problems for complete quasi-parabolic differential equations of odd order with variable domains of operators

We prove the well-posed solvability in the strong sense of the boundary value Problems

$$\begin{gathered} ( - 1)\frac{{_m d^{2m + 1} u}}{{dt^{2m + 1} }} + \sum\limits_{k = 0}^{m - 1} {\frac{{d^{k + 1} }}{{dt^{k + 1} }}} A_{2k + 1} (t)\frac{{d^k u}}{{dt^k }} + \sum\limits_{k = 1}^m {\frac{{d^k }}{{dt^k }}} A_{2k} (t)\frac{{d^k u}}{{dt^k }} + \lambda _m A_0 (t)u = f, \hfill \\ t \in ]0,t[,\lambda _m \geqslant 1, \hfill \\ {{d^i u} \mathord{\left/ {\vphantom {{d^i u} {dt^i }}} \right. \kern-\nulldelimiterspace} {dt^i }}|_{t = 0} = {{d^j u} \mathord{\left/ {\vphantom {{d^j u} {dt^j }}} \right. \kern-\nulldelimiterspace} {dt^j }}|_{t = T} = 0,i = 0,...,m,j = 0,...,m - 1,m = 0,1,..., \hfill \\ \end{gathered} $$

where the unbounded operators A _s (t), s > 0, in a Hilbert space H have domains D(A _s (t)) depending on t, are subordinate to the powers A ^1?(s?1)/2m (t) of some self-adjoint operators A(t) ≥ 0 in H, are [(s+1)/2] times differentiable with respect to t, and satisfy some inequalities. In the space H, the maximally accretive operators A ₀(t) and the symmetric operators A _s (t), s > 0, are approximated by smooth maximally dissipative operators B(t) in such a way that

$$\begin{gathered} \mathop {lim}\limits_{\varepsilon \to 0} Re(A_0 (t)B_\varepsilon ^{ - 1} (t)(B_\varepsilon ^{ - 1} (t))^ * u,u)_H = Re(A_0 (t)u,u)_H \geqslant c(A(t)u,u)_H \hfill \\ \forall u \in D(A_0 (t)),c > 0, \hfill \\ \end{gathered} $$

, where the smoothing operators are defined by

$$B_\varepsilon ^{ - 1} (t) = (I - \varepsilon B(t))^{ - 1} ,(B_\varepsilon ^{ - 1} (t)) * = (I - \varepsilon B^ * (t))^{ - 1} ,\varepsilon > 0.$$

.

     

Interlineation of functions of two variables on M(M>-2) lines preserving the class Cr(R2)

An algorithm for constructing the operator O_Mn({_kx}; x, y) with the properties

On a system of second order differential equations with periodic impulse coefficients

A thorough investigation of the systemd~2y(x):dx~2 p(x)y(x)=0with periodic impulse coefficientsp(x)={1,0≤xx_0>0) -η, x_0≤x<2π(η>0)p(x)=p(x 2π),-∞相似文献   

Analytic solution of vector model kinetic equations with constant kernel and their applications

Exact solutions are obtained for the first time for the half-space boundary-value problem for the vector model kinetic equations