A class of second-order neutral equations with deviating arguments are studied, and sufficient conditions are derived for every solution to be oscillatory.
The purpose of ibis paper is to study the distribution of zerocs of solutions of theneutral delay differential equations. An estimate is estublished for the distween betweenadjacenlt zeroes of the solutions of such eq...The purpose of ibis paper is to study the distribution of zerocs of solutions of theneutral delay differential equations. An estimate is estublished for the distween betweenadjacenlt zeroes of the solutions of such equations under less restritive hypotheses on the variable coefficients.The results obtained improve and extend scme known resultsin the literature.展开更多
Consider the neutral equation with variable coefficients dt[x(t) - P(t)x(t - γ)] + Q(t)x(t -σ) =0where P,Q∈C[[t0,,∞),R+] and σ,∈R+. We obtain some new sufficient conditions for the oscillation of soutions of the...Consider the neutral equation with variable coefficients dt[x(t) - P(t)x(t - γ)] + Q(t)x(t -σ) =0where P,Q∈C[[t0,,∞),R+] and σ,∈R+. We obtain some new sufficient conditions for the oscillation of soutions of the.abave equation without the restriction:0 P(t) 1 or P(t) 1.展开更多
We consider a system of neutral equations with unbounded delay, and derive conditions on Liapunov functionals to ensure that the solutions are uniformly bounded and uniformly ultimately bounded.
This paper focuses on the analytical and numerical asymptotical stability of neutral reaction-diffusion equations with piecewise continuous arguments.First,for the analytical solutions of the equations,we derive their...This paper focuses on the analytical and numerical asymptotical stability of neutral reaction-diffusion equations with piecewise continuous arguments.First,for the analytical solutions of the equations,we derive their expressions and asymptotical stability criteria.Second,for the semi-discrete and one-parameter fully-discrete finite element methods solving the above equations,we work out the sufficient conditions for assuring that the finite element solutions are asymptotically stable.Finally,with a typical example with numerical experiments,we illustrate the applicability of the obtained theoretical results.展开更多
This paper discusses a class of unstable second order neutral differential equations with positive and negative coeffcients. Sufficient conditions for all bounded solutions of the equations to be oscillatory are obtai...This paper discusses a class of unstable second order neutral differential equations with positive and negative coeffcients. Sufficient conditions for all bounded solutions of the equations to be oscillatory are obtained.展开更多
In this paper, the forced odd order neutral differential equations of the form are considered d n d t n[x(t)-R(t)x(t-τ)]+P(t)x(t-σ)=f(t),t≥t 0.A sufficient condition for the oscillation of all solutions is...In this paper, the forced odd order neutral differential equations of the form are considered d n d t n[x(t)-R(t)x(t-τ)]+P(t)x(t-σ)=f(t),t≥t 0.A sufficient condition for the oscillation of all solutions is obtained.展开更多
In this paper the perturbed neutral differential equation with positive and negative coefficientsddt[x(t)-C(t)x(t-r)]+P(t)x(t-τ)-Q(t)x(t-σ)=f(t,x(t)), t≥t 0is considered. Sufficient conditions for the zero soluti...In this paper the perturbed neutral differential equation with positive and negative coefficientsddt[x(t)-C(t)x(t-r)]+P(t)x(t-τ)-Q(t)x(t-σ)=f(t,x(t)), t≥t 0is considered. Sufficient conditions for the zero solution of this equation to be uniformly stable as well as asymptotically stable are obtained.展开更多
This paper has made researches on first order neutral differential equations with varia-ble coefficients and several deviations.The asymptotic behavior of nonoscillatory solutions of the equations are discussed.Necess...This paper has made researches on first order neutral differential equations with varia-ble coefficients and several deviations.The asymptotic behavior of nonoscillatory solutions of the equations are discussed.Necessary and sufficient conditions and several sufficient conditions for the oscillations of the equations are obtained.The relevent results in [1-3] are improved and genera-lized.展开更多
Existence criteria is established for the periodic solution of the nonlinear neutral delay differential equation x′(t)=f(t,x(t),x(t-τ 1(t)),x′(t-τ 2(t)))+p(t) by means of an abstract continuous theorem of k-set ...Existence criteria is established for the periodic solution of the nonlinear neutral delay differential equation x′(t)=f(t,x(t),x(t-τ 1(t)),x′(t-τ 2(t)))+p(t) by means of an abstract continuous theorem of k-set contractive operator and some analysis technique.展开更多
Some sufficient conditions are obtained for the oscillation of first order neutral differential_difference equations with positive and negative periodic coefficients.
In this paper, we discuss the existence and uniqueness of mild solutions of random impulsive abstract neutral partial differential equations in a real separable Hilbert space. The results are obtained by using Leray-S...In this paper, we discuss the existence and uniqueness of mild solutions of random impulsive abstract neutral partial differential equations in a real separable Hilbert space. The results are obtained by using Leray-Schauder Alternative and Banach Contraction Principle.Finally an example is given to illustrate our problem.展开更多
The aim of this paper is to study the asymptotic behavior of the oscillatory solutions of forced nonlinear neutral equations of the form[x(t)-∑mi=1p i(t)x(t-τ i)]′+∑nj=1q j(t)f(x(t-σ j))=r(t),t≥t 0,where p i,q ...The aim of this paper is to study the asymptotic behavior of the oscillatory solutions of forced nonlinear neutral equations of the form[x(t)-∑mi=1p i(t)x(t-τ i)]′+∑nj=1q j(t)f(x(t-σ j))=r(t),t≥t 0,where p i,q j,r∈C([t 0,∞),R),τ i,σ j≥0,i=1,2,…,m,j=1,2,…,n,f∈C(R,R),xf(x)>0 for x≠0. The results obtained here extend and improve some of the results of Ladas and Sficas [3] and J.R.Yan [5].展开更多
By means of an abstract continuation theorem, the existence criteria are established for the positive periodic solutions of a neutral functional differential equation d N d t=N(t)[a(t)-β(t)N(t)-b(t)N(t-σ(t))-c(...By means of an abstract continuation theorem, the existence criteria are established for the positive periodic solutions of a neutral functional differential equation d N d t=N(t)[a(t)-β(t)N(t)-b(t)N(t-σ(t))-c(t)N′(t-τ(t))].展开更多
The oscillatory behavior of neutral differential equation with positive and negative coefficients is investigated by mathematics analysis technique and the fixed point principle. Some sufficient conditions for oscilla...The oscillatory behavior of neutral differential equation with positive and negative coefficients is investigated by mathematics analysis technique and the fixed point principle. Some sufficient conditions for oscillation of neutral differential equation with positive and negative coefficients are obtained.展开更多
The article is concerned with oscillation of nonautonomous neutral dynamic delay equations on time scales. Sufficient conditions are established for the existence of bounded positive solutions and for oscillation of a...The article is concerned with oscillation of nonautonomous neutral dynamic delay equations on time scales. Sufficient conditions are established for the existence of bounded positive solutions and for oscillation of all solutions of this equation. Some results extend known results for difference equations when the time scale is the set Z^＋ of positive integers and for differential equations when the time scale is the set IR of real numbers.展开更多
Aim To investigate the existence of positive solutions for impulsive neutral differential equations. Methods The Banach contraction principle was used to establish our results. Results and Conclusion The results of...Aim To investigate the existence of positive solutions for impulsive neutral differential equations. Methods The Banach contraction principle was used to establish our results. Results and Conclusion The results of the existence of positive solutions for impulsive neutral differential equations are obtained.展开更多
文摘A class of second-order neutral equations with deviating arguments are studied, and sufficient conditions are derived for every solution to be oscillatory.
文摘The purpose of ibis paper is to study the distribution of zerocs of solutions of theneutral delay differential equations. An estimate is estublished for the distween betweenadjacenlt zeroes of the solutions of such equations under less restritive hypotheses on the variable coefficients.The results obtained improve and extend scme known resultsin the literature.
文摘Consider the neutral equation with variable coefficients dt[x(t) - P(t)x(t - γ)] + Q(t)x(t -σ) =0where P,Q∈C[[t0,,∞),R+] and σ,∈R+. We obtain some new sufficient conditions for the oscillation of soutions of the.abave equation without the restriction:0 P(t) 1 or P(t) 1.
文摘We consider a system of neutral equations with unbounded delay, and derive conditions on Liapunov functionals to ensure that the solutions are uniformly bounded and uniformly ultimately bounded.
文摘This paper focuses on the analytical and numerical asymptotical stability of neutral reaction-diffusion equations with piecewise continuous arguments.First,for the analytical solutions of the equations,we derive their expressions and asymptotical stability criteria.Second,for the semi-discrete and one-parameter fully-discrete finite element methods solving the above equations,we work out the sufficient conditions for assuring that the finite element solutions are asymptotically stable.Finally,with a typical example with numerical experiments,we illustrate the applicability of the obtained theoretical results.
文摘This paper discusses a class of unstable second order neutral differential equations with positive and negative coeffcients. Sufficient conditions for all bounded solutions of the equations to be oscillatory are obtained.
文摘In this paper, the forced odd order neutral differential equations of the form are considered d n d t n[x(t)-R(t)x(t-τ)]+P(t)x(t-σ)=f(t),t≥t 0.A sufficient condition for the oscillation of all solutions is obtained.
文摘In this paper the perturbed neutral differential equation with positive and negative coefficientsddt[x(t)-C(t)x(t-r)]+P(t)x(t-τ)-Q(t)x(t-σ)=f(t,x(t)), t≥t 0is considered. Sufficient conditions for the zero solution of this equation to be uniformly stable as well as asymptotically stable are obtained.
文摘This paper has made researches on first order neutral differential equations with varia-ble coefficients and several deviations.The asymptotic behavior of nonoscillatory solutions of the equations are discussed.Necessary and sufficient conditions and several sufficient conditions for the oscillations of the equations are obtained.The relevent results in [1-3] are improved and genera-lized.
文摘Existence criteria is established for the periodic solution of the nonlinear neutral delay differential equation x′(t)=f(t,x(t),x(t-τ 1(t)),x′(t-τ 2(t)))+p(t) by means of an abstract continuous theorem of k-set contractive operator and some analysis technique.
文摘Some sufficient conditions are obtained for the oscillation of first order neutral differential_difference equations with positive and negative periodic coefficients.
文摘In this paper, we discuss the existence and uniqueness of mild solutions of random impulsive abstract neutral partial differential equations in a real separable Hilbert space. The results are obtained by using Leray-Schauder Alternative and Banach Contraction Principle.Finally an example is given to illustrate our problem.
文摘The aim of this paper is to study the asymptotic behavior of the oscillatory solutions of forced nonlinear neutral equations of the form[x(t)-∑mi=1p i(t)x(t-τ i)]′+∑nj=1q j(t)f(x(t-σ j))=r(t),t≥t 0,where p i,q j,r∈C([t 0,∞),R),τ i,σ j≥0,i=1,2,…,m,j=1,2,…,n,f∈C(R,R),xf(x)>0 for x≠0. The results obtained here extend and improve some of the results of Ladas and Sficas [3] and J.R.Yan [5].
文摘In this paper, we obtain sufficient conditions for the oscillation of all solutionsof the nth-order neutral equation with continuous distributed delay
基金National Natural Science Foundation of China( 198710 0 5 )
文摘By means of an abstract continuation theorem, the existence criteria are established for the positive periodic solutions of a neutral functional differential equation d N d t=N(t)[a(t)-β(t)N(t)-b(t)N(t-σ(t))-c(t)N′(t-τ(t))].
文摘The oscillatory behavior of neutral differential equation with positive and negative coefficients is investigated by mathematics analysis technique and the fixed point principle. Some sufficient conditions for oscillation of neutral differential equation with positive and negative coefficients are obtained.
基金Project supported by the National Education Committee Doctoral Foundation of China (20020558092)
文摘The article is concerned with oscillation of nonautonomous neutral dynamic delay equations on time scales. Sufficient conditions are established for the existence of bounded positive solutions and for oscillation of all solutions of this equation. Some results extend known results for difference equations when the time scale is the set Z^＋ of positive integers and for differential equations when the time scale is the set IR of real numbers.
文摘Aim To investigate the existence of positive solutions for impulsive neutral differential equations. Methods The Banach contraction principle was used to establish our results. Results and Conclusion The results of the existence of positive solutions for impulsive neutral differential equations are obtained.
