共查询到20条相似文献,搜索用时 31 毫秒
1.
Giorgio Fusco 《Journal of Differential Equations》2011,250(7):3230-3279
We consider a regularization for a class of discontinuous differential equations arising in the study of neutral delay differential equations with state dependent delays. For such equations the possible discontinuity in the derivative of the solution at the initial point may propagate along the integration interval giving rise to so-called “breaking points”, where the solution derivative is again discontinuous. Consequently, the problem of continuing the solution in a right neighborhood of a breaking point is equivalent to a Cauchy problem for an ode with a discontinuous right-hand side (see e.g. Bellen et al., 2009 [4]). Therefore a classical solution may cease to exist.The regularization is based on the replacement of the vector-field with its time average over an interval of length ε>0. The regularized solution converges as ε→0+ to the classical Filippov solution (Filippov, 1964, 1988 [13] and [14]). Several properties of the solutions corresponding to small ε>0 are presented. 相似文献
2.
In this paper, we study the problem of global exponential stability for a class of impulsive neural networks with bounded and unbounded delays and fixed moments of impulsive effect. We establish stability criteria by employing Lyapunov functions and Razumikhin technique. An illustrative example is given to demonstrate the effectiveness of the obtained results. 相似文献
3.
The existence, uniqueness and continuous dependence of a mild solution of an impulsive neutral functional differential evolution nonlocal Cauchy problem in general Banach spaces are studied, by using the fixed point technique and semigroup of operators. 相似文献
4.
This paper deals with the existence of mild L-quasi-solutions to the initial value problem for a class of semilinear impulsive evolution equations in an ordered Banach space E. Under a new concept of upper and lower solutions, a new monotone iterative technique on the initial value problem of impulsive evolution equations has been established. The results improve and extend some relevant results in ordinary differential equations and partial differential equations. An example is also given. 相似文献
5.
The paper deals with an existence - uniqueness problem of the solution for functional differential equations with "maximums", Which arise in the theory of automatic control 相似文献
6.
S. A. Brykalov 《Georgian Mathematical Journal》1994,1(3):243-249
The paper gives sufficient conditions for the existence and nonuniqueness of monotone solutions of a nonlinear ordinary differential equation of the second order subject to two nonlinear boundary conditions one of which is two-point and the other is integral. The proof is based on an existence result for a problem with functional boundary conditions obtained by the author in [6]. 相似文献
7.
In this paper a generalization of the delayed exponential defined by Khusainov and Shuklin (2003) [1] for autonomous linear delay systems with one delay defined by permutable matrices is given for delay systems with multiple delays and pairwise permutable matrices. Using this multidelay-exponential a solution of a Cauchy initial value problem is represented. By an application of this representation and using Pinto’s integral inequality an asymptotic stability results for some classes of nonlinear multidelay differential equations are proved. 相似文献
8.
Piotr Rapp 《Aequationes Mathematicae》1991,41(1):136-160
Summary The problem of existence and uniqueness of solutions defined on the whole real line and satisfying given initial point data for general abstract linear functional differential equations is considered. The equation is not assumed to be of the delay type. The essence of the method presented here consists in the representation of a solution in the form analogous to the variation of constants formula known for linear ordinary differential equations. It is shown that such an approach can be effectively applied to the problem of existence and uniqueness of solutions satisfying an exponential growth estimate, provided that the deviation of the argument is sufficiently small. The proofs are based on the Banach fixed point principle. Detailed comparison and discussion of the hypotheses ensuring the existence and uniqueness of solutions are presented. 相似文献
9.
The aim of this paper is to establish the existence of solutions and some properties of set solutions for a Cauchy problem with causal operator in a separable Banach space. 相似文献
10.
Pedro Marín-Rubio José Real 《Nonlinear Analysis: Theory, Methods & Applications》2011,74(5):2012-2030
We prove the existence of solutions for a Navier-Stokes model in two dimensions with an external force containing infinite delay effects in the weighted space Cγ(H). Then, under additional suitable assumptions, we prove the existence and uniqueness of a stationary solution and the exponential decay of the solutions of the evolutionary problem to this stationary solution. Finally, we study the existence of pullback attractors for the dynamical system associated to the problem under more general assumptions. 相似文献
11.
The initial value problem is discussed for a class of linear functional differential equations of mixed type and various criteria on existence and uniqueness are obtained. 相似文献
12.
By using Krasnoselskii‘s fixed-point theorem on a suitable cone, several existence results and corresponding properties of positive solutions of nonlocal boundary value problem for nonlinear retarded differential equation are obtained. 相似文献
13.
This paper discusses the periodic boundary value problem for first-order nonlinear impulsive integro-differential equations. We prove some new comparison principles, and then establish new existence results for extremal solutions by using these principles and the monotone iterative technique. These results improve and extend all known relevant conclusions from the literature. Some examples are also given to illustrate the advantage of our results. 相似文献
14.
The paper deals with the existence-uniqueness problem of the solution of functional differential equations with maximums, which arises in the theory of automatic control. Making use of some previous results of the authors, sufficient conditions are obtained for the existence and uniqueness of the global solution of the initial value problem for these equations. 相似文献
15.
16.
In this paper, based on homotopy perturbation method (HPM) and reproducing kernel method (RKM), a new method is presented for solving nonlinear systems of second order boundary value problems (BVPs). HPM is based on the use of traditional perturbation method and homotopy technique. The HPM can reduce a nonlinear problem to a sequence of linear problems and generate a rapid convergent series solution in most cases. RKM is also an analytical technique, which can solve powerfully linear BVPs. Homotopy perturbation-reproducing kernel method (HP-RKM) combines advantages of these two methods and therefore can be used to solve efficiently systems of nonlinear BVPs. Three numerical examples are presented to illustrate the strength of the method. 相似文献
17.
Jehad O. Alzabut 《Journal of Computational and Applied Mathematics》2010,234(1):233-2097
By means of the contraction mapping principle and Gronwall-Bellman’s inequality, we prove the existence and exponential stability of positive almost periodic solution for an impulsive delay Nicholson’s blowflies model. The main results are illustrated by an example. 相似文献
18.
J. Frédéric Bonnans Audrey Hermant 《Annales de l'Institut Henri Poincaré (C) Analyse Non Linéaire》2009
This paper deals with the optimal control problem of an ordinary differential equation with several pure state constraints, of arbitrary orders, as well as mixed control-state constraints. We assume (i) the control to be continuous and the strengthened Legendre–Clebsch condition to hold, and (ii) a linear independence condition of the active constraints at their respective order to hold. We give a complete analysis of the smoothness and junction conditions of the control and of the constraints multipliers. This allows us to obtain, when there are finitely many nontangential junction points, a theory of no-gap second-order optimality conditions and a characterization of the well-posedness of the shooting algorithm. These results generalize those obtained in the case of a scalar-valued state constraint and a scalar-valued control. 相似文献
19.
By applying Mawhin’s continuation theory and some new inequalities, we obtain sufficient conditions for the existence of periodic solutions for a generalized high-order neutral differential equation in the critical case. Moreover, an example is given to illustrate the results. 相似文献
20.
Jan Čermák 《Georgian Mathematical Journal》1995,2(1):1-8
The aim of this paper is to find the class of continuous pointwise transformations (as general as possible) in the framework of which Kummer's transformationz(t)=g(t)y(h(t)) represents the most general pointwise transformation converting every linear homogeneous differential equation of thenth order into an equation of the same type. Further, some forms of these equations having certain subspaces of solutions are considered. 相似文献