共查询到20条相似文献,搜索用时 15 毫秒
1.
In this paper, we study the existence and some properties of solutions of the so-called set control differential equations (SCDE) and sheaf-solutions of sheaf set control problems. 相似文献
2.
Andreas Johann 《Journal of Differential Equations》2002,184(1):224-258
We investigate stationary and travelling wave solutions of a special lattice differential equation in one space dimension. Depending on a parameter λ, results are given on the existence, shape and stability for these kind of solutions. The analysis of travelling wave solutions leads us to a functional differential equation with both forward and backward shifts. The existence of solutions of this equation will be proved by use of the implicit function theorem. In particular, we consider kink solutions and periodic solutions. 相似文献
3.
B. van Brunt Hong Oh Kim Gregory Derfel 《Journal of Mathematical Analysis and Applications》2010,368(1):350-357
The pantograph equation is perhaps one of the most heavily studied class of functional differential equations owing to its numerous applications in mathematical physics, biology, and problems arising in industry. This equation is characterized by a linear functional argument. Heard (1973) [10] considered a generalization of this equation that included a nonlinear functional argument. His work focussed on the asymptotic behaviour of solutions for a real variable x as x→∞. In this paper, we revisit Heard's equation, but study it in the complex plane. Using results from complex dynamics we show that any nonconstant solution that is holomorphic at the origin must have the unit circle as a natural boundary. We consider solutions that are holomorphic on the Julia set of the nonlinear argument. We show that the solutions are either constant or have a singularity at the origin. There is a special case of Heard's equation that includes only the derivative and the functional term. For this case we construct solutions to the equation and illustrate the general results using classical complex analysis. 相似文献
4.
In this paper, a class of systems of matrix nonlinear differential equations containing as particular cases the systems of coupled Riccati differential equations arising in connection with control of some linear stochastic systems is considered.The system of differential equations considered in this paper are converted in a suitable nonlinear differential equation on a finite-dimensional Hilbert space adequately choosen.This allows us to use the positivity properties of the linear evolution operator defined by the linear differential equations of Lyapunov type.Our aim is to investigate properties of stabilizing and bounded solutions of the considered differential equations and to obtain some conditions ensuring the existence of such solutions.Conditions providing the existence of a maximal solution (minimal solution respectively) with respect to some classes of global solutions are presented. It is shown that if the coefficients of the equations are periodic functions all these special solutions (stabilizing, maximal, minimal) are periodic functions, too.Whenever possible the probabilistic arguments were avoided and so the results proved in the paper appear as results in the field of differential equations with interest in themselves. 相似文献
5.
Periodic solutions of abstract functional differential equations with state‐dependent delay 下载免费PDF全文
Filipe Andrade Claudio Cuevas Hernán R. Henríquez 《Mathematical Methods in the Applied Sciences》2016,39(13):3897-3909
In this paper, we are concerned with the existence of solutions of systems determined by abstract functional differential equations with infinite and state‐dependent delay. We establish the existence of mild solutions and the existence of periodic solutions. Our results are based on local Lipschitz conditions of the involved functions. We apply our results to study the existence of periodic solutions of a partial differential equation with infinite and state‐dependent delay. Copyright © 2016 John Wiley & Sons, Ltd. 相似文献
6.
Bruzón M. S. Gandarias M. L. Muriel C. Ramírez J. Saez S. Romero F. R. 《Theoretical and Mathematical Physics》2003,137(1):1367-1377
We use the classical and nonclassical methods to obtain symmetry reductions and exact solutions of the (2+1)-dimensional integrable Calogero–Bogoyavlenskii–Schiff equation. Although this (2+1)-dimensional equation arises in a nonlocal form, it can be written as a system of differential equations and, in potential form, as a fourth-order partial differential equation. The classical and nonclassical methods yield some exact solutions of the (2+1)-dimensional equation that involve several arbitrary functions and hence exhibit a rich variety of qualitative behavior. 相似文献
7.
We study a forward-backward system
of stochastic differential equations in an
infinite-dimensional framework and its relationships
with a semilinear parabolic differential equation on a Hilbert space,
in the spirit of the approach of Pardoux-Peng.
We prove that the stochastic system
allows us to construct a unique
solution of the parabolic equation in
a suitable class of locally Lipschitz real
functions. The parabolic equation is understood in
a mild sense which requires the notion
of a generalized directional gradient, that
we introduce by a probabilistic approach
and prove to exist for locally Lipschitz
functions.
The use of the generalized directional gradient
allows us to cover various applications to option
pricing problems and to optimal stochastic control problems
(including control of delay equations and
reaction--diffusion equations),
where the lack of differentiability of the coefficients
precludes differentiability of solutions to the associated
parabolic equations of Black--Scholes or Hamilton-Jacobi-Bellman
type. 相似文献
8.
Ahmet Bekir Özkan Güner Burcu Ayhan 《Mathematical Methods in the Applied Sciences》2015,38(17):3807-3817
In this paper, the ‐expansion method is proposed to establish hyperbolic and trigonometric function solutions for fractional differential‐difference equations with the modified Riemann–Liouville derivative. The fractional complex transform is proposed to convert a fractional partial differential‐difference equation into its differential‐difference equation of integer order. We obtain the hyperbolic and periodic function solutions of the nonlinear time‐fractional Toda lattice equations and relativistic Toda lattice system. The proposed method is more effective and powerful for obtaining exact solutions for nonlinear fractional differential–difference equations and systems. Copyright © 2014 John Wiley & Sons, Ltd. 相似文献
9.
《Mathematical Methods in the Applied Sciences》2018,41(7):2546-2574
This paper focuses on the construction of periodic solutions of nonlinear beam equations on the d‐dimensional tori. For a large set of frequencies, we demonstrate that an equivalent form of the nonlinear equations can be obtained by a para‐differential conjugation. Given the nonresonant conditions on each finite dimensional subspaces, it is shown that the periodic solutions can be constructed for the block diagonal equation by a classical iteration scheme. 相似文献
10.
Analysis of Fractional Differential Equations 总被引:3,自引:0,他引:3
Kai DiethelmNeville J. Ford 《Journal of Mathematical Analysis and Applications》2002,265(2):229-248
We discuss existence, uniqueness, and structural stability of solutions of nonlinear differential equations of fractional order. The differential operators are taken in the Riemann-Liouville sense and the initial conditions are specified according to Caputo's suggestion, thus allowing for interpretation in a physically meaningful way. We investigate in particular the dependence of the solution on the order of the differential equation and on the initial condition, and we relate our results to the selection of appropriate numerical schemes for the solution of fractional differential equations. 相似文献
11.
利用亚纯函数的Nevanlinna值分布理论,研究了一类复高阶微分方程的亚纯允许解的存在性问题.证明了在适当条件的假设下,该类复微分方程的亚纯解不是允许解的结果,推广了以前一些文献的结论,并且文中有例子表明结果是精确的. 相似文献
12.
László Simon 《Periodica Mathematica Hungarica》2008,56(1):143-156
We consider a system consisting of a quasilinear parabolic equation and a first order ordinary differential equation where
both equations contain functional dependence on the unknown functions. Then we consider a system which consists of a quasilinear
parabolic partial differential equation, a first order ordinary differential equation and an elliptic partial differential
equation. These systems were motivated by models describing diffusion and transport in porous media with variable porosity.
Supported by the Hungarian NFSR under grant OTKA T 049819. 相似文献
13.
H. Azad A. Laradji M. T. Mustafa 《Mathematical Methods in the Applied Sciences》2013,36(12):1615-1624
Conditions for the existence of polynomial solutions of certain second‐order differential equations have recently been investigated by several authors. In this paper, a new algorithmic procedure is given to determine necessary and sufficient conditions for a differential equation with polynomial coefficients containing parameters to admit polynomial solutions and to compute these solutions. The effectiveness of this approach is illustrated by applying it to determine new solutions of several differential equations of current interest. A comparative analysis is given to demonstrate the advantage of this algorithmic procedure over existing software. Copyright © 2012 John Wiley & Sons, Ltd. 相似文献
14.
Robert C. Dalang Olivier Lé vê que 《Transactions of the American Mathematical Society》2006,358(5):2123-2159
We study a class of hyperbolic stochastic partial differential equations in Euclidean space, that includes the wave equation and the telegraph equation, driven by Gaussian noise concentrated on a hyperplane. The noise is assumed to be white in time but spatially homogeneous within the hyperplane. Two natural notions of solutions are function-valued solutions and random field solutions. For the linear form of the equations, we identify the necessary and sufficient condition on the spectral measure of the spatial covariance for existence of each type of solution, and it turns out that the conditions differ. In spatial dimensions 2 and 3, under the condition for existence of a random field solution to the linear form of the equation, we prove existence and uniqueness of a random field solution to non-linear forms of the equation.
15.
Nonlinear BSDEs were first introduced by Pardoux and Peng, 1990, Adapted solutions of backward stochastic differential equations, Systems and Control Letters, 14, 51–61, who proved the existence and uniqueness of a solution under suitable assumptions on the coefficient. Fully coupled forward–backward stochastic differential equations and their connection with PDE have been studied intensively by Pardoux and Tang, 1999, Forward–backward stochastic differential equations and quasilinear parabolic PDE's, Probability Theory and Related Fields, 114, 123–150; Antonelli and Hamadène, 2006, Existence of the solutions of backward–forward SDE's with continuous monotone coefficients, Statistics and Probability Letters, 76, 1559–1569; Hamadème, 1998, Backward–forward SDE's and stochastic differential games, Stochastic Processes and their Applications, 77, 1–15; Delarue, 2002, On the existence and uniqueness of solutions to FBSDEs in a non-degenerate case, Stochastic Processes and Their Applications, 99, 209–286, amongst others. Unfortunately, most existence or uniqueness results on solutions of forward–backward stochastic differential equations need regularity assumptions. The coefficients are required to be at least continuous which is somehow too strong in some applications. To the best of our knowledge, our work is the first to prove existence of a solution of a forward–backward stochastic differential equation with discontinuous coefficients and degenerate diffusion coefficient where, moreover, the terminal condition is not necessary bounded. The aim of this work is to find a solution of a certain class of forward–backward stochastic differential equations on an arbitrary finite time interval. To do so, we assume some appropriate monotonicity condition on the generator and drift coefficients of the equation. The present paper is motivated by the attempt to remove the classical condition on continuity of coefficients, without any assumption as to the non-degeneracy of the diffusion coefficient in the forward equation. The main idea behind this work is the approximating lemma for increasing coefficients and the comparison theorem. Our approach is inspired by recent work of Boufoussi and Ouknine, 2003, On a SDE driven by a fractional brownian motion and with monotone drift, Electronic Communications in Probability, 8, 122–134; combined with that of Antonelli and Hamadène, 2006, Existence of the solutions of backward–forward SDE's with continuous monotone coefficients, Statistics and Probability Letters, 76, 1559–1569. Pursuing this idea, we adopt a one-dimensional framework for the forward and backward equations and we assume a monotonicity property both for the drift and for the generator coefficient. At the end of the paper we give some extensions of our result. 相似文献
16.
Summary We establish new comparison theorems on the oscillation of solutions of a class of perturbed half-linear differential equations.
These improve the work of Elbert and Schneider [6] in which connections are found between half-linear differential equations
and linear differential equations. Our comparison theorems are not of Sturm type or Hille--Wintner type which are very famous.
We can apply the main results in combination with Sturm's or Hille--Wintner's comparison theorem to a half-linear differential
equation of the general form (|x'|α-1x')' + a(t) |x|α-1x = 0. 相似文献
17.
研究偶次中立型泛函微分方程,给出了该微分方程解的振荡性的充分条件,得到了一些新的结果并给出了一些示例。 相似文献
18.
G. V. Demidenko V. A. Likhoshvai T. V. Kotova Yu. E. Khropova 《Siberian Mathematical Journal》2006,47(1):45-54
We establish a connection between solutions to a broad class of large systems of ordinary differential equations and solutions to retarded differential equations. We prove that solving the Cauchy problem for systems of ordinary differential equations reduces to solving the initial value problem for a retarded differential equation as the number of equations increases unboundedly. In particular, the class of systems under consideration contains a system of differential equations which arises in modeling of multiphase synthesis. 相似文献
19.
Consider the neutral delay differential equation [display math001] where [display math002] We studied the asymptotic behavior of the nonoscillatory solutions of Eq. (1) and we obtained sufficient conditions for the oscillation of all solutions, all bounded solutions, and all unbounded solutions of Eq. (1) 相似文献
20.
Gianni Manno Francesco Oliveri Raffaele Vitolo 《Journal of Mathematical Analysis and Applications》2007,332(2):767-786
We study the geometry of differential equations determined uniquely by their point symmetries, that we call Lie remarkable. We determine necessary and sufficient conditions for a differential equation to be Lie remarkable. Furthermore, we see how, in some cases, Lie remarkability is related to the existence of invariant solutions. We apply our results to minimal submanifold equations and to Monge-Ampère equations in two independent variables of various orders. 相似文献