The author aimed to investigate the solvability for nonlinear differential equations with not instantaneous impulses.Variational approach was adopted to obtain the existence of weak solutions as critical points. The f...The author aimed to investigate the solvability for nonlinear differential equations with not instantaneous impulses.Variational approach was adopted to obtain the existence of weak solutions as critical points. The findings of this study may serve as a reference for multiplicity of impulsive problems.展开更多
Nonlinear delay Caputo fractional differential equations with non-instantaneous impulses are studied and we consider the general case of delay,depending on both the time and the state variable.The case when the lower ...Nonlinear delay Caputo fractional differential equations with non-instantaneous impulses are studied and we consider the general case of delay,depending on both the time and the state variable.The case when the lower limit of the Caputo fractional derivative is fixed at the initial time,and the case when the lower limit of the fractional derivative is changed at the end of each interval of action of the impulse are studied.Practical stability properties,based on the modified Razumikhin method are investigated.Several examples are given in this paper to illustrate the results.展开更多
In this paper,existence and uniqueness of the solutions of the second order neutral differential equation with non-instantaneous impulses in a Hilbert space X are studied.This is followed by a brief discussion on the ...In this paper,existence and uniqueness of the solutions of the second order neutral differential equation with non-instantaneous impulses in a Hilbert space X are studied.This is followed by a brief discussion on the exact and trajectory controllability.Further,the strongly continuous cosine family of linear operators and Banach fixed point theorem are used to establish the results.Finally,an example is given to illustrate the analytical findings.展开更多
基金National Natural Science Foundations of China(No.11601143,11801160)School Level Scientific Research Project of Hunan First Normal University,China(No.XYS14N15)
文摘The author aimed to investigate the solvability for nonlinear differential equations with not instantaneous impulses.Variational approach was adopted to obtain the existence of weak solutions as critical points. The findings of this study may serve as a reference for multiplicity of impulsive problems.
基金supported by Portuguese funds through the CIDMA-Center for Research and Development in Mathematics and Applicationsthe Portuguese Foundation for Science and Technology(FCT-Fundação para a Ciência e a Tecnologia),within project UIDB/04106/2020Fund Scientific Research MU21FMI007,University of Plovdiv"Paisii Hilendarski".
文摘Nonlinear delay Caputo fractional differential equations with non-instantaneous impulses are studied and we consider the general case of delay,depending on both the time and the state variable.The case when the lower limit of the Caputo fractional derivative is fixed at the initial time,and the case when the lower limit of the fractional derivative is changed at the end of each interval of action of the impulse are studied.Practical stability properties,based on the modified Razumikhin method are investigated.Several examples are given in this paper to illustrate the results.
文摘In this paper,existence and uniqueness of the solutions of the second order neutral differential equation with non-instantaneous impulses in a Hilbert space X are studied.This is followed by a brief discussion on the exact and trajectory controllability.Further,the strongly continuous cosine family of linear operators and Banach fixed point theorem are used to establish the results.Finally,an example is given to illustrate the analytical findings.
