共查询到20条相似文献,搜索用时 15 毫秒
1.
We give sufficient conditions for the existence of extremal solutions to discontinuous and functional differential equations with impulses. Our main results are new even for ordinary differential equations without impulses. 相似文献
2.
Meiping Yao Aimin Zhao Jurang Yan 《Nonlinear Analysis: Theory, Methods & Applications》2009,71(9):4223-4230
This paper discusses first order functional differential equations with retardation and anticipation. By using the method of upper and lower solutions coupled with monotone iterative technique, new existence results are obtained which improve known results in the literature. 相似文献
3.
We apply the monotone iterative method to formulate existence results for integro-differential equations with nonlinear boundary conditions. Some results for integro-differential inequalities are also given. Examples illustrate obtained results. 相似文献
4.
Stability analysis of stochastic functional differential equations with infinite delay and its application to recurrent neural networks 总被引:1,自引:0,他引:1
Xiaodi Li 《Journal of Computational and Applied Mathematics》2010,234(2):407-417
In this paper, we investigate the stochastic functional differential equations with infinite delay. Some sufficient conditions are derived to ensure the pth moment exponential stability and pth moment global asymptotic stability of stochastic functional differential equations with infinite delay by using Razumikhin method and Lyapunov functions. Based on the obtained results, we further study the pth moment exponential stability of stochastic recurrent neural networks with unbounded distributed delays. The result extends and improves the earlier publications. Two examples are given to illustrate the applicability of the obtained results. 相似文献
5.
This paper is concerned with systems of impulsive second order delay differential equations. We prove that unstable systems can be stabilized by imposition of impulsive controls. The main tools used are Lyapunov functionals, stability theory and control by impulses. 相似文献
6.
7.
Mokhtar Kirane 《Nonlinear Analysis: Theory, Methods & Applications》2010,73(12):3723-235
We investigate the profile of the blowing-up solutions to the nonlinear nonlocal system (FDS):
8.
In this paper, we consider an initial value problem for a class of generalized ODEs, also known as Kurzweil equations, and we prove the existence of a local semidynamical system there. Under certain perturbation conditions, we also show that this class of generalized ODEs admits a discontinuous semiflow which we shall refer to as an impulsive semidynamical system. As a consequence, we obtain LaSalle's invariance principle for such a class of generalized ODEs. Due to the importance of LaSalle's invariance principle in studying stability of differential systems, we include an application to autonomous ordinary differential systems with impulse action at variable times. 相似文献
9.
Hassan A. El-Morshedy 《Nonlinear Analysis: Theory, Methods & Applications》2011,74(10):3353-3362
This paper contains new estimates for the distance between adjacent zeros of solutions of the first order delay differential equation
x′(t)+p(t)x(t−τ)=0 相似文献
10.
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
11.
We discuss the solvability of integral equations associated with initial value problems for a nonlinear differential equation of fractional order. The differential operator is the Caputo fractional derivative and the inhomogeneous term depends on the fractional derivative of lower orders. We obtain the existence of at least one solution for integral equations using the Leray–Schauder Nonlinear Alternative for several types of initial value problems. In addition, using the Banach contraction principle, we establish sufficient conditions for unique solutions. Our approach in obtaining integral equations is the “reduction” of the fractional order of the integro-differential equations based on certain semigroup properties of the Caputo operator. 相似文献
12.
Gani Tr. Stamov 《Nonlinear Analysis: Theory, Methods & Applications》2010,72(5):2457-2464
This paper studies the existence and uniqueness of exponentially stable almost periodic solutions for abstract impulsive differential equations in Banach space. The investigations are carried out by means of the fractional powers of operators. We construct an example to illustrate the feasibility of our results. 相似文献
13.
Oscillatory, nonoscillatory, and periodic solutions of re-tarded functional differential equations are investigated. The study concerns a system of two first order linear equations with piecewise constant argument. 相似文献
14.
Differential equations with impulses at random moments are set up and investigated. We study the case of Gamma distributed random moments of impulses. Several properties of solutions are studied based on properties of Gammma distributions. Some sufficient conditions for p-moment exponential stability of the solutions are given. 相似文献
15.
Oscillatory properties of retarded and advanced functional differential equations are investigated.In the first part, the study concerns equations with piecewise constant arguments, which found applications in certain biomedical problems. Then, results of some authors are generalized for general equations with many argument deviations. Finally, applications are given to equations with linear transformations of the argument. 相似文献
16.
Irina Shlykova Alexander Bulgakov 《Nonlinear Analysis: Theory, Methods & Applications》2011,74(11):3518-3530
Given a functional differential equation with a discontinuity, a construction of its extension in the shape of a functional differential inclusion is offered. This construction can be regarded as a generalization of the famous Filippov approach to study ordinary differential equations with discontinuities. Some basic properties of the solutions of the introduced functional differential inclusions are studied. The developed approach is applied to analysis of gene regulatory networks with general delays. 相似文献
17.
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
18.
In this paper, by using the generalization of Darbo’s fixed point theorem, we establish the existence of global solutions of an initial value problem for a class of second-order impulsive integro-differential equations of mixed type in a real Banach space. Our results generalize and improve on the results of Guo et al. [F. Guo, L.S. Liu, Y.H. Wu, P. Siew, Global solutions of initial value problems for nonlinear second-order impulsive integro-differential equations of mixed type in Banach spaces, Nonlinear Anal. 61 (2005) 1363–1382] in the sense that the conditions for existence of global solution in our theorem is simpler and less strict. To demonstrate the application of the theorem, we give the global solutions of two mixed boundary value problems for two classes of fourth order impulsive integro-differential equations. 相似文献
19.
Filippo Gazzola Raffaella Pavani 《Nonlinear Analysis: Theory, Methods & Applications》2011,74(17):6696-6711
We give strong theoretical and numerical evidence that solutions to some nonlinear fourth order ordinary differential equations blow up in finite time with infinitely many wild oscillations. We exhibit an explicit example where this phenomenon occurs. We discuss possible applications to biharmonic partial differential equations and to the suspension bridges model. In particular, we give a possible new explanation of the collapse of bridges. 相似文献
20.
The main purpose of this paper is to obtain the existence of
global solutions to semilinear integro-differential equations in Hilbert spaces
for rather general convolution kernels and nonlinear terms with superlinear
growth at infinity. The included application to a nonlinear model of heat
flow in materials of fading memory type provides motivations for the abstract
theory. 相似文献