In this paper,the approximate controllability of semilinear integrodifferential degenerate Sobolev equations with nonlocal conditions is investigated in the sense of integral solution in Hilbert spaces.Some sufficient...In this paper,the approximate controllability of semilinear integrodifferential degenerate Sobolev equations with nonlocal conditions is investigated in the sense of integral solution in Hilbert spaces.Some sufficient and necessary conditions are obtained.Firstly,the existence and uniqueness of integral solutions of semilinear integrodifferential degenerate Sobolev equations with nonlocal conditions are considered by GE-evolution operator theory and Sadovskii’s fixed point theorem,the existence and uniqueness theorem of solutions is given.Secondly,the approximate controllability of semilinear integrodifferential degenerate Sobolev equations with nonlocal conditions is studied in the sense of integral solution.The criterion for approximate controllability is provided.The obtained results have important theoretical and practical value for the study of controllability of semilinear integrodifferential degenerate Sobolev equations with nonlocal conditions.展开更多
In this paper, we establish sufficient conditions for the controllability of a class of semilinear impulsive integrodifferential systems with nonlocal initial conditions in Banach spaces. We derive the conditions usin...In this paper, we establish sufficient conditions for the controllability of a class of semilinear impulsive integrodifferential systems with nonlocal initial conditions in Banach spaces. We derive the conditions using Hausdorff measure of noncompactness, Sadovskii fixed point theorem and operator semigroups in particular dropping compactness of the operator.展开更多
In this paper, by means of Sadovskii fixed point theorem, the authors establish a result concerning the controllability for a class of abstract neutral functional differential systems where the linear part is non-dens...In this paper, by means of Sadovskii fixed point theorem, the authors establish a result concerning the controllability for a class of abstract neutral functional differential systems where the linear part is non-densely defined and satisfies the Hille-Yosida condition. As an application, an example is provided to illustrate the obtained result.展开更多
Many practical systems in physical and technical sciences have impulsive dynamical behaviors during the evolution process which can be modeled by impulsive differential equations. In this paper, we prove the approxima...Many practical systems in physical and technical sciences have impulsive dynamical behaviors during the evolution process which can be modeled by impulsive differential equations. In this paper, we prove the approximate controllability of control systems governed by a class of impulsive neutral stochastic functional differential system with state-dependent delay in Hilbert spaces. Sufficient conditions for approximate controllability of the control systems are established under the natural assumption that the corresponding linear system is approximately controllable. The results are obtained by using semigroup theory, stochastic analysis techniques, fixed point approach and abstract phase space axioms. An example is provided to illustrate the application of the obtained results.展开更多
基金supported by the National Natural Science Foundation of China under Grant Nos.12126401 and 11926402。
文摘In this paper,the approximate controllability of semilinear integrodifferential degenerate Sobolev equations with nonlocal conditions is investigated in the sense of integral solution in Hilbert spaces.Some sufficient and necessary conditions are obtained.Firstly,the existence and uniqueness of integral solutions of semilinear integrodifferential degenerate Sobolev equations with nonlocal conditions are considered by GE-evolution operator theory and Sadovskii’s fixed point theorem,the existence and uniqueness theorem of solutions is given.Secondly,the approximate controllability of semilinear integrodifferential degenerate Sobolev equations with nonlocal conditions is studied in the sense of integral solution.The criterion for approximate controllability is provided.The obtained results have important theoretical and practical value for the study of controllability of semilinear integrodifferential degenerate Sobolev equations with nonlocal conditions.
基金supported by University Grant Commission (UGC), India (No. G2/1287/UGC SAP DRS/2009)
文摘In this paper, we establish sufficient conditions for the controllability of a class of semilinear impulsive integrodifferential systems with nonlocal initial conditions in Banach spaces. We derive the conditions using Hausdorff measure of noncompactness, Sadovskii fixed point theorem and operator semigroups in particular dropping compactness of the operator.
基金Project supported by the Tianyuan Foundation of Mathematics (No. A0324624)the National Natural Science Founcation of China (No. 10371040)the Shanghai Priority Academic Discipline.
文摘In this paper, by means of Sadovskii fixed point theorem, the authors establish a result concerning the controllability for a class of abstract neutral functional differential systems where the linear part is non-densely defined and satisfies the Hille-Yosida condition. As an application, an example is provided to illustrate the obtained result.
基金supported by Indo-US Science and Technology Forum (IUSSTF), New Delhi, India and UGC Special Assistance Programme (SAP)DRS-Ⅱ,University Grants Commission, New Delhi, India (No. F.510/2/DRS/2009(SAP-Ⅰ)
文摘Many practical systems in physical and technical sciences have impulsive dynamical behaviors during the evolution process which can be modeled by impulsive differential equations. In this paper, we prove the approximate controllability of control systems governed by a class of impulsive neutral stochastic functional differential system with state-dependent delay in Hilbert spaces. Sufficient conditions for approximate controllability of the control systems are established under the natural assumption that the corresponding linear system is approximately controllable. The results are obtained by using semigroup theory, stochastic analysis techniques, fixed point approach and abstract phase space axioms. An example is provided to illustrate the application of the obtained results.
