Related papers: Unpredictable Solutions of Linear Differential Equ…
In the present paper we derive Liouville type results and existence of periodic solutions for $\chi^{(2)}$ type systems with non-homogeneous nonlinearities. Moreover, we prove both universal bounds as well as singularity and decay estimates…
In this paper, we study diagonalizable hyperbolic systems in one space dimension. Based on a new gradient entropy estimate, we prove the global existence of a continuous solution, for large and nondecreasing initial data. Moreover, we show…
In this paper, we have considered second order non-homogeneous linear differential equations having entire coefficients. We have established conditions ensuring non-existence of finite order solution of such type of differential equations.
In this paper we presents an algorithm for finding a solution of the linear nonhomogeneous quaternionic-valued differential equations. Moveover, several examples shows the feasibility of our algorithm.
A novel type of trajectory on semiflows, called asymptotically unpredictable, was proposed by Fen and Tokmak Fen [15]. The presence of sensitivity, which is an indispensable feature of chaotic dynamics, is a crucial property that arises…
The fundamental characteristics of soliton and chaos in nonlinear equation are completely different. But all nonlinear equations with a soliton solution may derive chaos. While only some equations with a chaos solution have a soliton. The…
The paper concerns boundary value problems for general nonautonomous first order quasilinear hyperbolic systems in a strip. We construct small global classical solutions, assuming that the right hand sides are small. In the case that all…
We discuss solution concepts for linear hyperbolic equations with coefficients of regularity below Lipschitz continuity. Thereby our focus is on theories which are based either on a generalization of the method of characteristics or on…
We consider the characteristic problem for the ultrahyperbolic equation in the Euclidean space. The value of a solution is prescribed on the characteristic hyperplane. A well-posed set-up of the problem is discussed. We obtain a certain…
We obtain global and local theorems on the existence of invariant manifolds for perturbations of non autonomous linear difference equations assuming a very general form of dichotomic behavior for the linear equation. The results obtained…
In this Note, we review the main existing results, methods, and some key open problems on the controllability of nonlinear hyperbolic and parabolic equations. Especially, we describe our recent universal approach to solve the local…
Linear differential equations of arbitrary order with polynomial coefficients are considered. Specifically, necessary and sufficient conditions for the existence of polynomial solutions of a given degree are obtained for these equations. An…
The paper considers a stochastic differential equation of Duffing type with Markov coefficients. The existence of unpredictable solutions is considered. The unpredictability is a property of bounded functions characterized by unbounded…
We consider nonlinear perturbations of the hyperbolic equation in the Hilbert space. Necessary and sufficient conditions for the existence of solutions of boundary-value problem for the corresponding equation and iterative procedures for…
In this paper we study the asymptotic behavior of nonoscillatory solutions for high order differential equations of Poincar\'e type. We introduce two new and more weak than classical hypotheses on the coefficients, which implies a well…
The periodic solutions of a type of nonlinear hyperbolic partial differential equations with a localized nonlinearity are investigated. For instance, these equations are known to describe several acoustical systems with fluid-structure…
We obtain global and local theorems on the existence of invariant manifolds for perturbations of non autonomous linear differential equations assuming a very general form of dichotomic behavior for the linear equation. Besides some new…
The paper contains a review of results on linear systems of ordinary differential equations of an arbitrary order on a finite interval with the most general inhomogeneous boundary conditions in Sobolev spaces. The character of the…
This article is devoted to the study of solutions of non-homogenous linear differential equations having entire coefficients. We get all non-trivial solutions of infinite order of equation $f^{(n)}+a_{n-1}(z)f^{(n-1)}+\ldots…
This paper approaches the question of existence and uniqueness of stationary solutions to a semilinear hyperbolic-parabolic system and the study of the asymptotic behaviour of global solutions. The system is a model for some biological…