This paper discusses the stability of theoretical solutions for nonlinear multi-variable delay perturbation problems (MVDPP) of the form x′(t)=f(x(t),x(t-τ 1(t)),...,x(t-τ m(t)),y(t),y(t-τ 1(t)),...,y(t-τ m(t...This paper discusses the stability of theoretical solutions for nonlinear multi-variable delay perturbation problems (MVDPP) of the form x′(t)=f(x(t),x(t-τ 1(t)),...,x(t-τ m(t)),y(t),y(t-τ 1(t)),...,y(t-τ m(t))), and εy′(t)=g(x(t),x(t-τ 1(t)),...,x(t-τ m(t)),y(t),y(t-τ 1(t)),...,y(t-τ m(t))), where 0<ε1. A sufficient condition of stability for the systems is obtained. Additionally we prove the numerical solutions of the implicit Euler method are stable under this condition.展开更多
The author presents a simple approach to both regularity and singularity theorems for free boundaries in classical obstacle problems.This approach is based on the monotonicity of several variational integrals,the Fede...The author presents a simple approach to both regularity and singularity theorems for free boundaries in classical obstacle problems.This approach is based on the monotonicity of several variational integrals,the Federer-Almgren dimension reduction and stratification theorems,and some simple PDE arguments.展开更多
In this paper,we consider the existence of positive solutions for the singular fourth-order four point boundary value problem with p-Laplacian operator.By using the fixed point theorem of cone expansion and compressio...In this paper,we consider the existence of positive solutions for the singular fourth-order four point boundary value problem with p-Laplacian operator.By using the fixed point theorem of cone expansion and compression,the existence of multiple positive solutions is ob-tained.展开更多
This paper studies a class of nonlinear singular systems with discontinuous right-hand sides,it develops nonsmooth Lyapunov stability theory as well as LaSalle invariance principle.In this paper,LaSalle invariance pri...This paper studies a class of nonlinear singular systems with discontinuous right-hand sides,it develops nonsmooth Lyapunov stability theory as well as LaSalle invariance principle.In this paper,LaSalle invariance principle of the discontinuous nonlinear singular systems is presented firstly.Furthermore,some sufficient conditions for stability and asymptotic stability of the given systems based on Filippov differential inclusion and Clarke's generalized gradient are given.Finally,these results are illustrated by the given example.展开更多
文摘This paper discusses the stability of theoretical solutions for nonlinear multi-variable delay perturbation problems (MVDPP) of the form x′(t)=f(x(t),x(t-τ 1(t)),...,x(t-τ m(t)),y(t),y(t-τ 1(t)),...,y(t-τ m(t))), and εy′(t)=g(x(t),x(t-τ 1(t)),...,x(t-τ m(t)),y(t),y(t-τ 1(t)),...,y(t-τ m(t))), where 0<ε1. A sufficient condition of stability for the systems is obtained. Additionally we prove the numerical solutions of the implicit Euler method are stable under this condition.
基金Project supported by the National Science Foundation (No.DMS 0700517)
文摘The author presents a simple approach to both regularity and singularity theorems for free boundaries in classical obstacle problems.This approach is based on the monotonicity of several variational integrals,the Federer-Almgren dimension reduction and stratification theorems,and some simple PDE arguments.
基金the National Natural Science Foundation of China (No.10671181)
文摘In this paper,we consider the existence of positive solutions for the singular fourth-order four point boundary value problem with p-Laplacian operator.By using the fixed point theorem of cone expansion and compression,the existence of multiple positive solutions is ob-tained.
基金supported by the National Natural Science Fundation of China under Grant No.60874006
文摘This paper studies a class of nonlinear singular systems with discontinuous right-hand sides,it develops nonsmooth Lyapunov stability theory as well as LaSalle invariance principle.In this paper,LaSalle invariance principle of the discontinuous nonlinear singular systems is presented firstly.Furthermore,some sufficient conditions for stability and asymptotic stability of the given systems based on Filippov differential inclusion and Clarke's generalized gradient are given.Finally,these results are illustrated by the given example.
