A new improvement of Hilbert's inequality for double series can be establishedby means of a strengthened Cauchy's inequality. As application, a quite sharp result onFejer-Riesz's inequality is obtained.
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
文摘A new improvement of Hilbert's inequality for double series can be establishedby means of a strengthened Cauchy's inequality. As application, a quite sharp result onFejer-Riesz's inequality is obtained.
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.
