To study a class of boundary value problems of parabolic differential equations with deviating arguments, averaging technique, Green’s formula and symbol function sign(·) are used. The multi dimensional problem...To study a class of boundary value problems of parabolic differential equations with deviating arguments, averaging technique, Green’s formula and symbol function sign(·) are used. The multi dimensional problem was reduced to a one dimensional oscillation problem for ordinary differential equations or inequalities. Two oscillatory criteria of solutions for systems of parabolic differential equations with deviating arguments are obtained.展开更多
Aim To study properties of solutions to a class of second order differential inequality with continuous distributed deviating arguments. Methods A direct analysis technique was used. Results and Conclusion Some suf...Aim To study properties of solutions to a class of second order differential inequality with continuous distributed deviating arguments. Methods A direct analysis technique was used. Results and Conclusion Some sufficient conditions that ensure a class of second order delay differential inequality having no eventually positive solutions were obtained, which generalized some given results. Using the results, some oscillatory criteria for solutions of the hyperbolic equation with distributed deviating arguments can be established.展开更多
Based on Mansevich-Mawhin continuation theorem and some analysis skill,some sufficient conditions for the existence of periodic solutions for mixed type p-Laplacian equation with deviating arguments are established,...Based on Mansevich-Mawhin continuation theorem and some analysis skill,some sufficient conditions for the existence of periodic solutions for mixed type p-Laplacian equation with deviating arguments are established,which are complement of previously known results.展开更多
By means of Mawhin's continuation theorem,we study a kind of lie'nard functional differential equations:x"(t)+f(x(t))x'(t)+g(t,x(t-τ(t))) = e(t).Some new results on the existence and uniqueness of pe...By means of Mawhin's continuation theorem,we study a kind of lie'nard functional differential equations:x"(t)+f(x(t))x'(t)+g(t,x(t-τ(t))) = e(t).Some new results on the existence and uniqueness of periodic solutions are obtained.展开更多
By using the theory of coincidence degree, we study a kind of periodic solutions to second order differential equation with a deviating argument such as x″(t) + f(x′(t)) + h(x(t))x′(t) + g(x(t - τ...By using the theory of coincidence degree, we study a kind of periodic solutions to second order differential equation with a deviating argument such as x″(t) + f(x′(t)) + h(x(t))x′(t) + g(x(t - τ(t))) ≈ p(t), some sufficient conditions on the existence of periodic solutions are obtained.展开更多
In this paper, by using the continuation theorem of coincidence degree theory and some analysis methods, we study a kind of periodic solutions to p-Laplacian neutral functional differential equation with a deviating a...In this paper, by using the continuation theorem of coincidence degree theory and some analysis methods, we study a kind of periodic solutions to p-Laplacian neutral functional differential equation with a deviating argument,some new results on the existence of periodic solutions is obtained.展开更多
A class of hyperbolic equations with continuous distributed deviating arguments is considered and its oscillation theorems are discussed.These theorems are of higher degree of generality and deal with the cases which ...A class of hyperbolic equations with continuous distributed deviating arguments is considered and its oscillation theorems are discussed.These theorems are of higher degree of generality and deal with the cases which are not covered by the known criteria.Particularly,these criteria extend and unify a number of existing results.展开更多
Aim To study a class of boundary value problem of hyperbolic partial functional differential equations with continuous deviating arguments. Methods An averaging technique was used. The multi dimensional problem was...Aim To study a class of boundary value problem of hyperbolic partial functional differential equations with continuous deviating arguments. Methods An averaging technique was used. The multi dimensional problem was reduced to a one dimensional oscillation problem for ordinary differential equations or inequalities. Results and Conclusion The known results of oscillation of solutions for a class of boundary value problem of hyperbolic partial functional differential equations with discrete deviating arguments are generalized, and the oscillatory criteria of solutions for such equation with two kinds of boundary value conditions are obtained.展开更多
In this paper,the oscillation of solutions of hyperbolic partial functional differential equations is studied,and oscillatory criteria of solutions with three kinds of boundary conditions are obtained.
In this paper, we will study the oscillatory properties of the second order half-linear dynamic equations with distributed deviating arguments on time scales. We obtain several new sufficient conditions for the oscill...In this paper, we will study the oscillatory properties of the second order half-linear dynamic equations with distributed deviating arguments on time scales. We obtain several new sufficient conditions for the oscillation of all solutions of this equation. Our results not only unify the oscillation of second order nonlinear differential and difference equations but also can be applied to different types of time scales with sup T = ∞. Our results improve and extend some known results in the literature. Examples which dwell upon the importance of our results are also included.展开更多
A model was proposed for addressing investment risk of the flee reserve in the form of credit or currency risk. This risk was expressed by a constant amount K ( e. g., securitization) upon an interest-increasing eve...A model was proposed for addressing investment risk of the flee reserve in the form of credit or currency risk. This risk was expressed by a constant amount K ( e. g., securitization) upon an interest-increasing event and a random variable Z representing the recovery rate of a bond or a devaluation factor. The model equation is an integro-differential equation with deviating arguments. The analytical solutions were obtained for the probability of survival as Z is a discrete random variable and as Z is a continuous random variable respectively.展开更多
A class of second-order neutral equations with deviating arguments are studied, and sufficient conditions are derived for every solution to be oscillatory.
Even order neutral functional differential equations are considered. Sufficient conditions for the oscillation behavior of solutions for this differential equation are presented. The new results are presented and some...Even order neutral functional differential equations are considered. Sufficient conditions for the oscillation behavior of solutions for this differential equation are presented. The new results are presented and some examples are also given.展开更多
By using the continuation theorem of coincidence degree theory due to Mawhin and the new analytical method, we study the T-periodic solutions to a class of third order p-Laplacian equations with distributed delays as ...By using the continuation theorem of coincidence degree theory due to Mawhin and the new analytical method, we study the T-periodic solutions to a class of third order p-Laplacian equations with distributed delays as follows . Some new results for existence of T-periodic solutions to such equations are obtained.展开更多
By using the method of coincidence degree and Lyapunov functional, a set ofeasily applicable criteria are established for the global existence and global asymptotic stabilityof strictly positive (componentwise) period...By using the method of coincidence degree and Lyapunov functional, a set ofeasily applicable criteria are established for the global existence and global asymptotic stabilityof strictly positive (componentwise) periodic solution of a periodic n-species Lotka-Volterracompetition system with feedback controls and several deviating arguments. The problem considered inthis paper is in many aspects more general and incorporate as special cases various problems whichhave been studied extensively in the literature. Moreover, our new criteria, which improve andgeneralize some well known results, can be easily checked.展开更多
In this paper,we use the Leray-Schauder degree theory to establish some new results on the existence and uniqueness of anti-periodic solutions to an nth-order nonlinear differential equation with multiple deviating ar...In this paper,we use the Leray-Schauder degree theory to establish some new results on the existence and uniqueness of anti-periodic solutions to an nth-order nonlinear differential equation with multiple deviating arguments.展开更多
By using the theory of coincidence degree, we study a kind of periodic solution to p-Laplacian differential equation with a deviating argument such as (φp(x'(t)))' + f(x(t)) + g(x(t - τ(t))) = e...By using the theory of coincidence degree, we study a kind of periodic solution to p-Laplacian differential equation with a deviating argument such as (φp(x'(t)))' + f(x(t)) + g(x(t - τ(t))) = e(t), a result on the existence of periodic solution is obtained.展开更多
By the methods of differential inequality and eigenvalue, we obtain several sufficient conditions for oscillation of solutions for higher-order impulsive hyperbolic system with distributed deviating arguments under Ro...By the methods of differential inequality and eigenvalue, we obtain several sufficient conditions for oscillation of solutions for higher-order impulsive hyperbolic system with distributed deviating arguments under Robin and Dirichlet boundary value conditions.展开更多
In this paper, we study a class of higher order nonlinear integro-diferential equations with deviating arguments. With the aid of the integral inequality, we obtain some sufcient conditions under which all solutions t...In this paper, we study a class of higher order nonlinear integro-diferential equations with deviating arguments. With the aid of the integral inequality, we obtain some sufcient conditions under which all solutions to the equation have some asymptotic behavior.展开更多
文摘To study a class of boundary value problems of parabolic differential equations with deviating arguments, averaging technique, Green’s formula and symbol function sign(·) are used. The multi dimensional problem was reduced to a one dimensional oscillation problem for ordinary differential equations or inequalities. Two oscillatory criteria of solutions for systems of parabolic differential equations with deviating arguments are obtained.
文摘Aim To study properties of solutions to a class of second order differential inequality with continuous distributed deviating arguments. Methods A direct analysis technique was used. Results and Conclusion Some sufficient conditions that ensure a class of second order delay differential inequality having no eventually positive solutions were obtained, which generalized some given results. Using the results, some oscillatory criteria for solutions of the hyperbolic equation with distributed deviating arguments can be established.
基金Foundation item: Supported by the Foundation of Education Department of Jiangxi Province(G J J11234) Supported by the Natural Science Foundation of Jiangxi Province(2009GQS0023) Supported by the Natural Science Foundation of Shangrao Normal University(1001)
文摘Based on Mansevich-Mawhin continuation theorem and some analysis skill,some sufficient conditions for the existence of periodic solutions for mixed type p-Laplacian equation with deviating arguments are established,which are complement of previously known results.
基金Foundation item: Supported by the Anhui Natural Science Foundation(050460103) Supported by the NSF of Anhui Educational Bureau(KJ2008B247) Supported by the RSPYT of Anhui Educational Bu- reau(2008jq1111)
文摘By means of Mawhin's continuation theorem,we study a kind of lie'nard functional differential equations:x"(t)+f(x(t))x'(t)+g(t,x(t-τ(t))) = e(t).Some new results on the existence and uniqueness of periodic solutions are obtained.
基金the Natural Science Foundation of Anhui Province(050460103)the Natural Science Foundation by the Bureau of Education of Anhui Province(2005kj031ZD)
文摘By using the theory of coincidence degree, we study a kind of periodic solutions to second order differential equation with a deviating argument such as x″(t) + f(x′(t)) + h(x(t))x′(t) + g(x(t - τ(t))) ≈ p(t), some sufficient conditions on the existence of periodic solutions are obtained.
基金Supported by the Key NSF of the Education Ministry of China(2007047)Supported by the Scientific Research Foundation of NUIST(09022)
文摘In this paper, by using the continuation theorem of coincidence degree theory and some analysis methods, we study a kind of periodic solutions to p-Laplacian neutral functional differential equation with a deviating argument,some new results on the existence of periodic solutions is obtained.
基金Supported by the NNSF of China(A011403)Supported by the Young Teachers Science Foundation of Beijing University of Civil Engineering and Architecture(100804107)
文摘A class of hyperbolic equations with continuous distributed deviating arguments is considered and its oscillation theorems are discussed.These theorems are of higher degree of generality and deal with the cases which are not covered by the known criteria.Particularly,these criteria extend and unify a number of existing results.
文摘Aim To study a class of boundary value problem of hyperbolic partial functional differential equations with continuous deviating arguments. Methods An averaging technique was used. The multi dimensional problem was reduced to a one dimensional oscillation problem for ordinary differential equations or inequalities. Results and Conclusion The known results of oscillation of solutions for a class of boundary value problem of hyperbolic partial functional differential equations with discrete deviating arguments are generalized, and the oscillatory criteria of solutions for such equation with two kinds of boundary value conditions are obtained.
文摘In this paper,the oscillation of solutions of hyperbolic partial functional differential equations is studied,and oscillatory criteria of solutions with three kinds of boundary conditions are obtained.
文摘In this paper, we will study the oscillatory properties of the second order half-linear dynamic equations with distributed deviating arguments on time scales. We obtain several new sufficient conditions for the oscillation of all solutions of this equation. Our results not only unify the oscillation of second order nonlinear differential and difference equations but also can be applied to different types of time scales with sup T = ∞. Our results improve and extend some known results in the literature. Examples which dwell upon the importance of our results are also included.
基金Project supported by National Natural Science Foundation of China (Grant Nos. 10471088, 60572126)
文摘A model was proposed for addressing investment risk of the flee reserve in the form of credit or currency risk. This risk was expressed by a constant amount K ( e. g., securitization) upon an interest-increasing event and a random variable Z representing the recovery rate of a bond or a devaluation factor. The model equation is an integro-differential equation with deviating arguments. The analytical solutions were obtained for the probability of survival as Z is a discrete random variable and as Z is a continuous random variable respectively.
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Even order neutral functional differential equations are considered. Sufficient conditions for the oscillation behavior of solutions for this differential equation are presented. The new results are presented and some examples are also given.
基金Foundation item: Supported by the National Natural Science Foundation of China(ll07100t) Supported by the 211 Project of Anhui University(KJTD002B) Supported by the Natural Science Foundation of Anhui Province(t208085MAB)
文摘By using the continuation theorem of coincidence degree theory due to Mawhin and the new analytical method, we study the T-periodic solutions to a class of third order p-Laplacian equations with distributed delays as follows . Some new results for existence of T-periodic solutions to such equations are obtained.
文摘By using the method of coincidence degree and Lyapunov functional, a set ofeasily applicable criteria are established for the global existence and global asymptotic stabilityof strictly positive (componentwise) periodic solution of a periodic n-species Lotka-Volterracompetition system with feedback controls and several deviating arguments. The problem considered inthis paper is in many aspects more general and incorporate as special cases various problems whichhave been studied extensively in the literature. Moreover, our new criteria, which improve andgeneralize some well known results, can be easily checked.
基金supported by the National Natural Science Foundation of China (10771001)the NSF of Educational Bureau of Anhui Province (KJ2009A005Z+2 种基金KJ2010B124)the NSF of Anhui Province (090416237)the Characteristic Speciality of Mathematics Education in Anhui Province and the Young Talents Support of Anhui Province (2010SQRL159)
文摘In this paper,we use the Leray-Schauder degree theory to establish some new results on the existence and uniqueness of anti-periodic solutions to an nth-order nonlinear differential equation with multiple deviating arguments.
基金This research was supported by Natural Science Foundation of Anhui Province (No.050460103)Natural Science Foundation by the Bureau of Education of Anhui Province (No.2005kj031ZD).
文摘By using the theory of coincidence degree, we study a kind of periodic solution to p-Laplacian differential equation with a deviating argument such as (φp(x'(t)))' + f(x(t)) + g(x(t - τ(t))) = e(t), a result on the existence of periodic solution is obtained.
基金This work is supported by the National Natural Sciences Foundation of China under Grant 10361006 and the Natural Sciences Foundation of Yunnan Province under Grant 2003A0001M.
文摘By the methods of differential inequality and eigenvalue, we obtain several sufficient conditions for oscillation of solutions for higher-order impulsive hyperbolic system with distributed deviating arguments under Robin and Dirichlet boundary value conditions.
文摘In this paper, we study a class of higher order nonlinear integro-diferential equations with deviating arguments. With the aid of the integral inequality, we obtain some sufcient conditions under which all solutions to the equation have some asymptotic behavior.