In this paper author studies the solvability of abstract hopulsive differential equations on Banach space X. By terms of integrated bisendgroup, author obtains the existence of abstract impulsive differential equation...In this paper author studies the solvability of abstract hopulsive differential equations on Banach space X. By terms of integrated bisendgroup, author obtains the existence of abstract impulsive differential equations with finite contant impulses and gives a condition which makes the impulsive equation be solvable for a Variable impuls.展开更多
In this paper, the notions of integral Φ0-stability of ordinary impulsive differential equations are introduced. The definition of integral Φ0-stability depends significantly on the fixed time impulses. Sufficient c...In this paper, the notions of integral Φ0-stability of ordinary impulsive differential equations are introduced. The definition of integral Φ0-stability depends significantly on the fixed time impulses. Sufficient conditions for integral Φ0-stability are obtained by using comparison principle and piecewise continuous cone valued Lyapunov functions. A new comparison lemma, connecting the solutions of given impulsive differential system to the solution of a vector valued impulsive differential system is also established.展开更多
Some properties of integrated bisemigroup S(t) of linear operators on a Banach space X are studied. The structure of the positive and negative subspaces and the operation of integrated bisemigroup on corresponding dif...Some properties of integrated bisemigroup S(t) of linear operators on a Banach space X are studied. The structure of the positive and negative subspaces and the operation of integrated bisemigroup on corresponding differentiable subspace C-n are established. respectively. The decomposition of the infinitesimal generator A of S(t) and other interested problems are also considered. As application, an abstract boundary value problem is discussed.展开更多
In this work, we investigate the solvability of the boundary value problem for the Poisson equation, involving a generalized Riemann-Liouville and the Caputo derivative of fractional order in the class of smooth funct...In this work, we investigate the solvability of the boundary value problem for the Poisson equation, involving a generalized Riemann-Liouville and the Caputo derivative of fractional order in the class of smooth functions. The considered problems are generalization of the known Dirichlet and Neumann oroblems with operators of a fractional order.展开更多
The behavior of beams with variable stiffness subjected to the action of variable loadings (impulse or harmonic) is analyzed in this paper using the successive approximation method. This successive approximation metho...The behavior of beams with variable stiffness subjected to the action of variable loadings (impulse or harmonic) is analyzed in this paper using the successive approximation method. This successive approximation method is a technique for numerical integration of partial differential equations involving both the space and time, with well-known initial conditions on time and boundary conditions on the space. This technique, although having been applied to beams with constant stiffness, is new for the case of beams with variable stiffness, and it aims to use a quadratic parabola (in time) to approximate the solutions of the differential equations of dynamics. The spatial part is studied using the successive approximation method of the partial differential equations obtained, in order to transform them into a system of time-dependent ordinary differential equations. Thus, the integration algorithm using this technique is established and applied to examples of beams with variable stiffness, under variable loading, and with the different cases of supports chosen in the literature. We have thus calculated the cases of beams with constant or variable rigidity with articulated or embedded supports, subjected to the action of an instantaneous impulse and harmonic loads distributed over its entire length. In order to justify the robustness of the successive approximation method considered in this work, an example of an articulated beam with constant stiffness subjected to a distributed harmonic load was calculated analytically, and the results obtained compared to those found numerically for various steps (spatial h and temporal τ ¯ ) of calculus, and the difference between the values obtained by the two methods was small. For example for ( h=1/8 , τ ¯ =1/ 64 ), the difference between these values is 17%.展开更多
A variation of parameters formula with Green function type and Gronwall type integral inequality are proved for impulsive differential equations involving piecewise constant delay of generalized type. Some results for...A variation of parameters formula with Green function type and Gronwall type integral inequality are proved for impulsive differential equations involving piecewise constant delay of generalized type. Some results for piecewise constant linear and nonlinear delay differential equations with impulsive effects are obtained.They include existence and uniqueness theorems, a variation of parameters formula, integral inequalities, the oscillation property and some applications.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
文摘In this paper author studies the solvability of abstract hopulsive differential equations on Banach space X. By terms of integrated bisendgroup, author obtains the existence of abstract impulsive differential equations with finite contant impulses and gives a condition which makes the impulsive equation be solvable for a Variable impuls.
文摘In this paper, the notions of integral Φ0-stability of ordinary impulsive differential equations are introduced. The definition of integral Φ0-stability depends significantly on the fixed time impulses. Sufficient conditions for integral Φ0-stability are obtained by using comparison principle and piecewise continuous cone valued Lyapunov functions. A new comparison lemma, connecting the solutions of given impulsive differential system to the solution of a vector valued impulsive differential system is also established.
基金the National Key Project of China the Natural Science Foundation of Shanxi
文摘Some properties of integrated bisemigroup S(t) of linear operators on a Banach space X are studied. The structure of the positive and negative subspaces and the operation of integrated bisemigroup on corresponding differentiable subspace C-n are established. respectively. The decomposition of the infinitesimal generator A of S(t) and other interested problems are also considered. As application, an abstract boundary value problem is discussed.
文摘In this work, we investigate the solvability of the boundary value problem for the Poisson equation, involving a generalized Riemann-Liouville and the Caputo derivative of fractional order in the class of smooth functions. The considered problems are generalization of the known Dirichlet and Neumann oroblems with operators of a fractional order.
文摘The behavior of beams with variable stiffness subjected to the action of variable loadings (impulse or harmonic) is analyzed in this paper using the successive approximation method. This successive approximation method is a technique for numerical integration of partial differential equations involving both the space and time, with well-known initial conditions on time and boundary conditions on the space. This technique, although having been applied to beams with constant stiffness, is new for the case of beams with variable stiffness, and it aims to use a quadratic parabola (in time) to approximate the solutions of the differential equations of dynamics. The spatial part is studied using the successive approximation method of the partial differential equations obtained, in order to transform them into a system of time-dependent ordinary differential equations. Thus, the integration algorithm using this technique is established and applied to examples of beams with variable stiffness, under variable loading, and with the different cases of supports chosen in the literature. We have thus calculated the cases of beams with constant or variable rigidity with articulated or embedded supports, subjected to the action of an instantaneous impulse and harmonic loads distributed over its entire length. In order to justify the robustness of the successive approximation method considered in this work, an example of an articulated beam with constant stiffness subjected to a distributed harmonic load was calculated analytically, and the results obtained compared to those found numerically for various steps (spatial h and temporal τ ¯ ) of calculus, and the difference between the values obtained by the two methods was small. For example for ( h=1/8 , τ ¯ =1/ 64 ), the difference between these values is 17%.
文摘A variation of parameters formula with Green function type and Gronwall type integral inequality are proved for impulsive differential equations involving piecewise constant delay of generalized type. Some results for piecewise constant linear and nonlinear delay differential equations with impulsive effects are obtained.They include existence and uniqueness theorems, a variation of parameters formula, integral inequalities, the oscillation property and some applications.
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.
