Existence and uniqueness of solutions for the nonlinear impulsive fractional differential equations

In this paper, we investigate existence and uniqueness of solutions for nonlinear impulsive fractional differential equations. By utilizing the well-known fixed point theorems, we obtain some sufficient conditions for the uniqueness and existence of the solutions. At the end of the paper, an example is given to illustrate our main results.     

Existence,uniqueness and boundedness results for impulsive delay differential equations

This paper considers general impulsive delay differential equations. By utilizing a non-classical approach, the theory of existence and uniqueness of solutions are developed. Criteria on boundedness of solutions are also established through the use of Lyapunov functionals.     

Existence and uniqueness results for impulsive functional differential equations with scalar multiple delay and infinite delay

In this paper, we discuss local and global existence and uniqueness results for first order impulsive functional differential equations with multiple delay. We shall rely on a nonlinear alternative of Leray–Schauder. For the global existence and uniqueness we apply a recent nonlinear alternative of Leray–Schauder type in Fréchet spaces, due to M. Frigon and A. Granas [Résultats de type Leray–Schauder pour des contractions sur des espaces de Fréchet, Ann. Sci. Math. Québec 22 (2) (1998) 161–168]. The goal of this paper is to extend the problems considered by A. Ouahab [Local and global existence and uniqueness results for impulsive differential equations with multiple delay, J. Math. Anal. Appl. 323 (2006) 456–472].     

Existence and uniqueness of mild solutions to impulsive fractional differential equations

This paper is concerned with the existence and uniqueness of a mild solution to impulsive fractional semilinear differential equations. The results are obtained by means of fixed point methods. We also give an example of such problems.     

Existence of solutions for impulsive partial neutral functional differential equations

This paper is concerned with partial neutral functional differential equations of first and second order with impulses. We establish some results of existence of mild solutions for these classes of equations.     

非线性一阶常微分方程解的存在惟一性

讨论了一类非线性一阶常微分方程边值问题解的存在惟一性.得到了当参数在一定的范围取值时解存在惟一的充分条件,并包含了一些已知结果.主要结果基于Leray-Schauder非线性抉择理论和Banach不动点定理.     

Existence of solutions for nonlinear impulsive differential equations with Dirichlet boundary conditions

In this paper, we consider the existence of solutions for a class of nonlinear impulsive problems with Dirichlet boundary conditions. We obtain some new existence theorems of solutions for the nonlinear impulsive problem by using critical point theory. We extend and improve some recent results.     

Existence of solutions for impulsive partial neutral functional differential equation with infinite delay

In this paper, the existence of mild solutions for first-order impulsive semilinear neutral functional differential equations with infinite delay in Banach spaces is investigated. We derive conditions in respect of the Hausdorff measure of noncompactness under which the mild solutions exist in Banach spaces. Our results improve and generalize some previous results.     

Existence and uniqueness of optimal solutions for multirate partial differential algebraic equations

The numerical simulation of electric circuits including multirate signals can be done by a model based on partial differential algebraic equations. In the case of frequency modulated signals, a local frequency function appears as a degree of freedom in the model. Thus the determination of a solution with a minimum amount of variation is feasible, which allows for resolving on relatively coarse grids. We prove the existence and uniqueness of the optimal solutions in the case of initial-boundary value problems as well as biperiodic boundary value problems. The minimisation problems are also investigated and interpreted in the context of optimal control. Furthermore, we construct a method of characteristics for the computation of optimal solutions in biperiodic problems. Numerical simulations of test examples are presented.     

Existence of global solutions for second order impulsive abstract partial differential equations

In this paper, we study the existence of global solutions for a class of second order impulsive abstract functional differential equations. The results are obtained by using Leray-Schauder’s Alternative fixed point theorem. An application is provided to illustrate the theory.     

Existence of solutions for nonlinear boundary value problems of impulsive differential equations

With the help of the coincidence degree continuation theorem, we generalize to the case of impulsive systems of the second order some existence results obtained by Gaines and Mawhin in the ordinary case. In particular, for the impulsive functions the treatment does not assume any monotonicity conditions, which are necessary in earlier papers treated by S.Hu and V.Lakshmikantham, L.H.Erbe and X.Liu with other methods.     

脉冲时滞差分方程非振动解的存在性

讨论脉冲时滞差分方程 给出了由时滞差分方程非振动解的存在性刻划出相应的脉冲时滞差分方程的同样性质的一般性脉冲条件。     

Existence and uniqueness of solutions to neutral stochastic functional differential equations with infinite delay

This paper investigates the existence and uniqueness theorem of solutions to neutral stochastic differential equations with infinite delay (short for INSFDEs) at a space BC((-∞,0];R^d). Under the uniform Lipschitz condition, linear growth condition is weaken to obtain the moment estimate of the solution for INSFDEs. Furthermore, the existence, uniqueness theorem of the solution for INSFDEs is derived, and the estimate for the error between approximate solution and exact solution is given. On the other hand, under the linear growth condition, the uniform Lipschitz condition is replaced by the local Lipschitz condition, the existence, uniqueness theorem is also valid for INSFDEs on [t₀,T]. Moreover, the existence, uniqueness theorem still holds on interval [t₀,∞), where t₀∈R is an arbitrary real number.     

Existence of positive solutions of nonlinear fractional delay differential equations

This paper investigates the existence and uniqueness of positive solutions for a class of nonlinear fractional delay differential equations. Using a nonlinear alternative of Leray-Schauder type, we show the existence of positive solutions for the equations in question.     

Periodic solutions of delay impulsive differential equations

We study the following semilinear impulsive differential equation with delay:

     

Flow invariance for solutions to nonlinear nonautonomous partial differential delay equations

We investigate the problem of existence and flow invariance of mild solutions to nonautonomous partial differential delay equations , t?s, us=φ, where B(t) is a family of nonlinear multivalued, α-accretive operators with D(B(t)) possibly depending on t, and the operators F(t,.) being defined—and Lipschitz continuous—possibly only on “thin” subsets of the initial history space E. The results are applied to population dynamics models. We also study the asymptotic behavior of solutions to this equation. Our analysis will be based on the evolution operator associated to the equation in the initial history space E.     

Existence and uniqueness of solutions of initial value problems for nonlinear fractional differential equations

In this paper, by using the fixed point theory, we study the existence and uniqueness of initial value problems for nonlinear fractional differential equations and obtain a new result.     

Existence results for impulsive neutral functional differential equations with infinite delay

In this work, we prove the existence of mild solutions for impulsive partial neutral functional differential equations with infinite delay in a Banach space. The results are obtained by using the Krasnoselski–Schaefer type fixed point theorem.     

EXISTENCE OF SOLUTIONS FOR SECONDORDER IMPULSIVE DIFFERENTIAL EQUATIONS

In this paper, we apply the coincidence degree theory to study nonlinear second orderimPulsive periodic boundary value problems (PBVP), and show some sufficient conditions for the existence of solutions.