A Kind of Cover Layer Phenomenon of Solution for the Singularly Perturbed Problem with Third Order Nonlinear Equation

利用微分不等式理论研究了一类三阶非线性奇摄动问题解的套层现象。得到了问题解的一致有效的渐近展开式。

THE SINGULARLY PERTURBED BOUNDARY VALUE PROBLEMS FOR HIGHER ORDER SEMILINEAR ELLIPTIC EQUATIONS

In this paper a singular perturbation of boundary value problem for elliptic partial differential equations of higher order is considered by using the differential inequalities. The uniformly valid asymptotic expansion in entire region is obtained.

OSCILLATION THEOREMS FOR SECOND ORDER QUASILINEAR PERTURBED DIFFERENTIAL EQUATIONS

New oscillation criteria for the second order perturbed differential equation are presented. The special case of the results includes the corresponding results in previous papers, extends and unifies a number of known results.

Asymptotic solution for a class of weakly nonlinear singularly perturbed reaction diffusion problem

Under appropriate conditions, with the perturbation method and the theory of differential inequalities, a class of weakly nonlinear singularly perturbed reaction diffusion problem is considered. The existence of solution of the original problem is proved by constructing the auxiliary functions. The uniformly valid asymptotic expansions of the solution for arbitrary mth order approximation are obtained through constructing the formal solutions of the original problem, expanding the nonlinear terms to the power in small parameter ε and comparing the coefficient for the same powers of ε. Finally, an example is provided, resulting in the error of 0（ε^2）.

A Class of Strongly Nonlinear Singular Perturbed Boundary Value Problems

In this paper,a class of strongly nonlinear singular perturbed boundary value problems are considered by the theory of differential inequalities and the correction of boundary layer,under which the existence of solution is proved and the uniformly valid asymptotic expansions is obtained as well.

A Class of Nonlinear Singularly Perturbed Problems of Fourth Order

A class of fourth order singularly perturbed boundary value problems are studied. The existence of solution and its uniformly valid asymptotic estimation are obtained.

BOUNDARY AND INTERIOR LAYER BEHAVIOR FOR SINGULARLY PERTURBED VECTOR PROBLEM

In this paper, we consider the vector nonlinear boundary value problem:where is a small parameter,f and g are continuous functions in R4 Under appropriate assumptions, by means of the differential inequalities, we demonstrate the existence and estimation, involving boundary and interior layers, of the solutions to the above problem.

BOUNDARY AND INTERIOR LAYER PHENOMENA OF SINGULARLY PERTURBED NONLINEAR ELLIPTIC PROBLEMS

This paper investigates the boundary value problems for a class of singularly perturbed nonlinear elliptic equations. By means of the theory of partial differential in- equalities the author obtains the existence and asymptotic estimation of the solutions, involving the boundary and interior layer behavior, of the problems as described.

THE SINGULARLY PERTURBED NONLINEAR BOUNDARY VALUE PROBLEMS

The singularly perturbed nonlinear boundary value problems are considered.Using the stretched variable and the method of boundary layer correction,the formal asymptotic expansion of solution is obtained.And then the uniform validity of solution is proved by using the differential inequalities.

Singularly Perturbed Solution of Three Species Volterra Model with Constant Harvest and Invest Rates

In this paper, we consider the three species Volterra model of the first-order nonlinear differential equations. Using the method of multiple scales, the.asymptotic expansions of solution for the original problem are obtained, and the uniformly valid asymptotic estimations of the solution are discussed.

A KIND OF SINGULARLY PERTURBED BOUNDARY VALUE PROBLEM FOR NONLINEAR VOLTERRA FUNCTIONAL DIFFERENTIAL EQUATIONS

In this paper,a kind of boundary value problems for Volterra functional differential equation is studied.\$\$εx″(t)=f(t,x(t),\(t),x(t-τ),x′(t),ε),t∈(0,1), x(t)=φ(t,ε),t∈[-τ,0], ax(1)+bx′(1)=A(ε).\$\$\ \ By using the theory of differential inequality,the author proves the existence of the solutions and a uniformly valid asymptotic expansion of the solution is given as well.

THE SINGULARLY PERTURBED NONLOCAL BOUNDARY VALUE PROBLEMS FOR HIGHER ORDER NONLINEAR ELLIPTIC EQUATIONS

In this paper,a class of singular perturbation of nonlocal boundary value problems for elliptic partial differential equations of higher order is considered by using the differential inequalities.The uniformly valid asymptotic expansion of solution is obtained.

奇异摄动区间变时滞不确定非线性系统稳定性分析

奇异摄动系统是实际问题中普遍存在的一类系统,为了使此类系统在应用上达到一定的稳定,利用矩阵分块方法对含有不确定结构的奇异摄动区间变时滞非线性系统稳定性进行分析,通过构造新的Lyapunov函数,基于Lyapunov稳定性理论,结合舒尔补引理、积分不等式和线性矩阵不等式等方法推出奇异摄动系统在摄动参数界内时滞相关的稳定性判据.

Delay-range-dependent Stability Criterion for Interval Time-delay Systems with Nonlinear Perturbations

In this paper, we consider the problem of robust stability for a class of linear systems with interval time-varying delay under nonlinear perturbations using Lyapunov-Krasovskii （LK） functional approach. By partitioning the delay-interval into two segments of equal length, and evaluating the time-derivative of a candidate LK functional in each segment of the delay-interval, a less conservative delay-dependent stability criterion is developed to compute the maximum allowable bound for the delay-range within which the system under consideration remains asymptotically stable. In addition to the delay-bi-segmentation analysis procedure, the reduction in conservatism of the proposed delay-dependent stability criterion over recently reported results is also attributed to the fact that the time-derivative of the LK functional is bounded tightly using a newly proposed bounding condition without neglecting any useful terms in the delay-dependent stability analysis. The analysis, subsequently, yields a stable condition in convex linear matrix inequality （LMI） framework that can be solved non-conservatively at boundary conditions using standard numerical packages. Furthermore, as the number of decision variables involved in the proposed stability criterion is less, the criterion is computationally more effective. The effectiveness of the proposed stability criterion is validated through some standard numerical examples.

Improved Exponential Stability Criteria for Uncertain Neutral System with Nonlinear Parameter Perturbations

This paper investigates the problem of robust exponential stability for neutral systems with time-varying delays and nonlinear perturbations. Based on a novel Lyapunov functional approach and linear matrix inequality technique, a new delay-dependent stability condition is derived. Since the model transformation and bounding techniques for cross terms are avoided, the criteria proposed in this paper are less conservative than some previous approaches by using the free-weighting matrices. One numerical example is presented to illustrate the effectiveness of the proposed results.

An Improved Robust Model Predictive Control Approach to Systems with Linear Fractional Transformation Perturbations

In this paper, a robust model predictive control approach is proposed for a class of uncertain systems with time-varying, linear fractional transformation perturbations. By adopting a sequence of feedback control laws instead of a single one, the control performance can be improved and the region of attraction can be enlarged compared with the existing model predictive control （MPC） approaches. Moreover, a synthesis approach of MPC is developed to achieve high performance with lower on-line computational burden. The effectiveness of the proposed approach is verified by simulation examples.

Delay-dependent robust stabilization for a class ofneutral systems with nonlinear perturbations

This note deals with the problem of stabilization/stability for neutral systems with nonlinear perturbations. A new stabilization/stability scheme is presented. Using improved Lyapunov functionals, less conservative stabilization/stability conditions are derived for such systems based on linear matrix inequalities （LMI）. Numerical examples are provided to show that the proposed results significantly improve the allowed upper bounds of the delay size over some existing ones in the literature.

Singular Perturbations for a Class of Fourth-order Nonlinear Boundary Value Problem

这份报纸被奉献学习下列不可思议地使不安第四顺序的平常的微分方程 ey ( 4 )= f ( t ， y ， y ， y )， 0 t 1 ， 0 第1wi 非线性的边界条件 y ( 0 )= y ( 1 )= 0 ， p ( y “( 0 )， y ”( 0 ))= 0 ， q ( y “( 1 )， y ( 1 ))= 0where f ：[0， 1 ]?? 潣潣牥楣敶洠灡楰杮?????????????????? 僚 ??? 汩敢瑲？？