微分系统的稳定性

This article deals with the reflecting function of the differential systems.The results are applied to discuss the stability of these differential systems.     

Influence of Multiple Micro Cracks on the Damage Behavior of a Macro-Crack Tip北大核心CSCD

The solution of an infinite plane containing a macro crack and a cluster of micro cracks under uniaxial tensile load was presented based on Muskhelishvili’s complex function method and the stepwise recursive method. The stress field and stress intensity factor K were obtained. Combined with the damage mechanics, damage parameter D of the macro-crack tip and the micro-crack tip under uniaxial tension was redefined, and the influence of different damage zone forms on the damage of the crack tip was analyzed. The results show that, both the chain-distribution and the reverse-chain-distribution micro cracks have an amplifying effect on the macro crack growth, and the damage parameter increases with the decrease of the inclination angle of the micro crack and the reduction of the distance between the macro crack and the micro cracks. For a relatively small inclination angle of the micro crack, the damage parameters of the macro crack and the micro crack heightens, and the damage parameter of the macro crack increases with the micro-crack length. For evenly distributed micro cracks in the continuous damage zone, the micro cracks have an amplifying effect on the macro-crack growth, and the damage parameter of the macro crack increases with the micro-crack number. © 2022 Editorial Office of Applied Mathematics and Mechanics. All rights reserved.     

Positively expansive differentiable maps

We study the space of positively expansive differentiable maps of a compact connected C ∞ Riemannian manifold without boundary. It is proved that （i） the C1-interior of the set of positively expansive differentiable maps coincides with the set of expanding maps, and （ii） Cl-generically, a differentiable map is positively expansive if and only if it is expanding.     

A Line Search and Trust Region Algorithm with Trust Region Radius Converging to Zero

In this paper, we present a new line search and trust region algorithm for unconstrained optimization problem with the trust region radius converging to zero. The new trust region algorithm performs a backtracking line search from the failed, point instead of resolving the subproblem when the trial step results in an increase in the objective function. We show that the algorithm preserves the convergence properties of the traditional trust region algorithms. Numerical results are also given.     

THE SOLVABILITY FOR NONLINEAR SINGULARLY PERTURBED DIFFERENTIAL SYSTEM

The solvability for the nonlinear singularly perturbed boundary value pro- blem of differential system is considered.Using the boundary layer corrective method the formal asymptotic solution is constructed.And using the theory of differential inequality proves the uniform validity of the asymptotic expansion for the solution.     

支撑函数与Banach空间范数的可微性

In this paper,we defined a new continuity of supporting function and studyed a new convexity,smoothness of Banach Space and from this we studyed the relations among such convexity,smoothness and differentiability of the norm of Banach Space.     

On Boundary-Value Problems for the Laplacian in Bounded Domains with Micro Inhomogeneous Structure of the Boundaries

We consider boundary-value problems with rapidly alternating types of boundary conditions. We present the classification of homogenized （limit） problems depending on the ratio of small parameters, which characterize the diameter of parts of the boundary with different types of boundary conditions. Also we study the respective spectral problem of this type.     

The nonlinear boundary value problem for a class of integro-differential system

In this paper, using the theory of differential inequalities, we study the nonlinear boundary value problem for a class of integro-differential system. Under appropriate assumptions, the existence of solution is proved and the uniformly valid asymptotic expansions for arbitrary n-th order approximation and the estimation of remainder term are obtained simply and conveniently.     

Global Convergence of a Modified Gradient Projection Method for Convex Constrained Problems

In this paper, the continuously differentiable optimization problem min{f（x） ： x∈Ω}, where Ω ∈ R^n is a nonempty closed convex set, the gradient projection method by Calamai and More （Math. Programming, Vol.39. P.93-116, 1987） is modified by memory gradient to improve the convergence rate of the gradient projection method is considered. The convergence of the new method is analyzed without assuming that the iteration sequence {x^k} of bounded. Moreover, it is shown that, when f（x） is pseudo-convex （quasiconvex） function, this new method has strong convergence results. The numerical results show that the method in this paper is more effective than the gradient projection method.     

WAVEFORM RELAXATION METHODS OF NONLINEAR INTEGRAL-DIFFERENTIAL-ALGEBRAIC EQUATIONS

In this paper we consider continuous-time and discrete-time waveform relaxation meth-ods for general nonlinear integral-differential-algebraic equations. For the continuous-time case we derive the convergence condition of the iterative methods by invoking the spec-tral theory on the resulting iterative operators. By use of the implicit difference forms,namely the backward-differentiation formulae, we also yield the convergence condition of the discrete waveforms. Numerical experiments are provided to illustrate the theoretical work reported here.     

On a conservative integral equation with two kernels

We study the solvability of the integral equation

The existence of multiple positive solutions of p-Laplacian boundary value problems

In this paper, we establish sufficient conditions to guarantee the existence of at least three or 2n − 1 positive solutions of nonlocal boundary value problems consisting of the second-order differential equation with p-Laplacian

FINITE TRAVELING WAVES FOR A REACTION-DIFFUSION SYSTEM WITH N（≥3） COMPONENTS

ＦＩＮＩＴＥＴＲＡＶＥＬＩＮＧＷＡＶＥＳＦＯＲＡＲＥＡＣＴＩＯＮ┐ＤＩＦＦＵＳＩＯＮＳＹＳＴＥＭＷＩＴＨＮ（３）ＣＯＭＰＯＮＥＮＴＳＷＡＮＧＳＨＵ,ＷＥＮＳＨＩＨＬＩＡＮＧＡＮＤＹＥＱＩＸＩＡＯＡｂｓｔｒａｃｔ．Ｉｎｔｈｉｓｐａｐｅｒ,ｔｈｅｅｘ...     

Oscillation for systems of nonlinear neutral type parabolic partial functional differential equations

This paper discusses the oscillation of solutions for systems of nonlinear neutral type parabolic partial fuctional differential equations of the form     

Boundedness of solutions for sublinear reversible systems

We are concerned with the boundedness of all the solutions for second order differential equation

一类二阶渐近周期微分方程的正同宿轨道

§ 1　IntroductionIn this note we are concerned with the asymptotically periodic second order equation-u″+α( x) u =β( x) uq +γ( x) up,　 x∈ R,( 1 )where1 相似文献   

On oscillation and asymptotic behaviour of solutions of forced first order neutral differential equations

In this paper, sufficient conditions have been obtained under which every solution of

中立型二阶非线性微分方程振动性的判据

Abstract. In this paper ,the oscillation criteria for the solutions of the nonlinear differential e-quations of neutral type of the forms:     

Exact inequalities for derivatives of functions of low smoothness defined on an axis and a semiaxis

We obtain new exact inequalities of the form

Positive solutions for some 1-dimensional boundary value problems of Laplace-type

This paper deals with the existence of triple positive solutions for the 1-dimensional equation of Laplace-type(φ(x'(t)))' q(t)f(t,x(t),x'(t)) = 0, t ∈ (0, 1),subject to the following boundary condition:a1φ(x(0)) - a2φ(x'(0)) = 0, a3φ(x(1)) a4φ(x'(1)) = 0,where φ is an odd increasing homogeneous homeomorphism. By using a new fixed point theorem,sufficient conditions are obtained that guarantee the existence of at least three positive solutions. The emphasis here is that the nonlinear term f is involved with the first order derivative explicitly.