In this paper, the author discusses the multiple positive solutions for an infinite boundary value problem of first order impulsive superlinear integro-differential equations on the half line by means of the fixed poi...In this paper, the author discusses the multiple positive solutions for an infinite boundary value problem of first order impulsive superlinear integro-differential equations on the half line by means of the fixed point theorem of cone expansion and compression with norm type.展开更多
In this paper, the author discusses the multiple positive solutions for an infinite boundary value problem of first order impulsive singular integro-differential equations on the half line by means of the fixed point ...In this paper, the author discusses the multiple positive solutions for an infinite boundary value problem of first order impulsive singular integro-differential equations on the half line by means of the fixed point theorem of cone expansion and compression with norm type.展开更多
In this paper,the existence and uniqueness of iterative solutions to the boundary value problems for a class of first order impulsive integro-differential equations were studied. Under a new concept of upper and lower...In this paper,the existence and uniqueness of iterative solutions to the boundary value problems for a class of first order impulsive integro-differential equations were studied. Under a new concept of upper and lower solutions, a new monotone iterative technique on the boundary value problem of integro-differential equations was proposed. The existence and uniqueness of iterative solutions and the error estimation in certain interval were obtained.An example was also given to illustrate the results.展开更多
Under loose conditions, the existence of solutions to initial value problem are studied for second order impulsive integro-differential equation with infinite moments of impulse effect on the positive half real axis i...Under loose conditions, the existence of solutions to initial value problem are studied for second order impulsive integro-differential equation with infinite moments of impulse effect on the positive half real axis in Banach spaces. By the use of recurrence method, Tonelii sequence and the locally convex topology, the new existence theorems are achieved, which improve the related results obtained by Guo Da-jun.展开更多
In this paper, by establishing a new comparison result and using the monotone iterative technique, the existence of maximal and minimal solutions of the boundary value problem for second-order impulsive differential e...In this paper, by establishing a new comparison result and using the monotone iterative technique, the existence of maximal and minimal solutions of the boundary value problem for second-order impulsive differential equation which depends on x’ in Banach space is obtained.展开更多
In this paper, the stability of an impulsive integro-differential equation with finite and infinite delays is investigated. By applying the Lyapunov-Razumikin method, sufficient condition for global exponential stabil...In this paper, the stability of an impulsive integro-differential equation with finite and infinite delays is investigated. By applying the Lyapunov-Razumikin method, sufficient condition for global exponential stability of such equation is obtained.展开更多
By developing a comparison result and using the monotone iterative technique, we obtain the existence of the minimal and the maximal solutions to an integral boundary value problem for first order impulsive integro-di...By developing a comparison result and using the monotone iterative technique, we obtain the existence of the minimal and the maximal solutions to an integral boundary value problem for first order impulsive integro-differential equations.展开更多
This paper is concerned with the approximate controllability of nonlinear fractional impulsive neutral stochastic integro-differential equations with nonlocal conditions and infinite delay in Hilbert spaces under the ...This paper is concerned with the approximate controllability of nonlinear fractional impulsive neutral stochastic integro-differential equations with nonlocal conditions and infinite delay in Hilbert spaces under the assumptions that the corresponding linear system is approximately controllable. By the Krasnoselskii-Schaefer-type fixed point theorem and stochastic analysis theory, some sufficient conditions are given for the approximate controllability of the system. At the end, an example is given to illustrate the application of our result.展开更多
文摘In this paper, the author discusses the multiple positive solutions for an infinite boundary value problem of first order impulsive superlinear integro-differential equations on the half line by means of the fixed point theorem of cone expansion and compression with norm type.
基金supported by the National Nature Science Foundation of China (10671167)
文摘In this paper, the author discusses the multiple positive solutions for an infinite boundary value problem of first order impulsive singular integro-differential equations on the half line by means of the fixed point theorem of cone expansion and compression with norm type.
基金National Natural Science Foundation of China(No.11271372)Hunan Provincial National Natural Science Foundation of China(No.12JJ2004)Central South University Graduate Innovation Project,China(No.2014zzts136)
文摘In this paper,the existence and uniqueness of iterative solutions to the boundary value problems for a class of first order impulsive integro-differential equations were studied. Under a new concept of upper and lower solutions, a new monotone iterative technique on the boundary value problem of integro-differential equations was proposed. The existence and uniqueness of iterative solutions and the error estimation in certain interval were obtained.An example was also given to illustrate the results.
基金Project supported by the National Natural Science Foundation of China(Nos. 10572057 and 10251001)the Science Foundation of Nanjing University of Aeronautics and Austronautics
文摘Under loose conditions, the existence of solutions to initial value problem are studied for second order impulsive integro-differential equation with infinite moments of impulse effect on the positive half real axis in Banach spaces. By the use of recurrence method, Tonelii sequence and the locally convex topology, the new existence theorems are achieved, which improve the related results obtained by Guo Da-jun.
基金Foundation item: Science Foundation of Shanxi Province 20051009 and 2006011013.
文摘In this paper, by establishing a new comparison result and using the monotone iterative technique, the existence of maximal and minimal solutions of the boundary value problem for second-order impulsive differential equation which depends on x’ in Banach space is obtained.
基金supported by the Science Foundation of the Department of Science and Technology,Shandong Province (J10LA51 J11LA51 and 2010RKGA2051)
文摘In this paper, the stability of an impulsive integro-differential equation with finite and infinite delays is investigated. By applying the Lyapunov-Razumikin method, sufficient condition for global exponential stability of such equation is obtained.
基金supported by Natural Science Foundation of Hunan (No.09JJ6010)
文摘By developing a comparison result and using the monotone iterative technique, we obtain the existence of the minimal and the maximal solutions to an integral boundary value problem for first order impulsive integro-differential equations.
文摘This paper is concerned with the approximate controllability of nonlinear fractional impulsive neutral stochastic integro-differential equations with nonlocal conditions and infinite delay in Hilbert spaces under the assumptions that the corresponding linear system is approximately controllable. By the Krasnoselskii-Schaefer-type fixed point theorem and stochastic analysis theory, some sufficient conditions are given for the approximate controllability of the system. At the end, an example is given to illustrate the application of our result.
