Related papers: A new class of solvable nonlinear difference equat…
A system of inhomogeneous second-order difference equations with linear parts given by noncommutative matrix coefficients are considered. Closed form of its solution is derived by means of newly defined delayed matrix sine/cosine using the…
A generalization of the already studied transformations of the linear differential equation into a system of the first order equations is given. The proposed transformation gives possibility to get new forms of the N-dimensional system of…
For nonnegative real numbers $\alpha$, $\beta$, $\gamma$, $A$, $B$ and $C$ such that $B+C>0$ and $\alpha+\beta+\gamma >0$, the difference equation \begin{equation*} x_{n+1}=\displaystyle\frac{\alpha +\beta x_{n}+\gamma x_{n-1}}{A+B x_{n}+C…
The paper takles a procedure which allow to extend some linear, wave type equations to the study of nonlinear models. More concretely, we present a practical way to generate the largest class of a given form of second order differential…
The present paper refers to the theory and the practice of the systems regarding non-linear systems and their applications. We aimed the integration of these systems to elaborate their response as well as to highlight some outstanding…
We consider systems of polynomial equations and inequalities in $\mathbb{Q}[\boldsymbol{y}][\boldsymbol{x}]$ where $\boldsymbol{x} = (x_1, \ldots, x_n)$ and $\boldsymbol{y} = (y_1, \ldots,y_t)$. The $\boldsymbol{y}$ indeterminates are…
We consider the fundamental problem of solving quadratic systems of equations in $n$ variables, where $y_i = |\langle \boldsymbol{a}_i, \boldsymbol{x} \rangle|^2$, $i = 1, \ldots, m$ and $\boldsymbol{x} \in \mathbb{R}^n$ is unknown. We…
Symmetry groups allow to transform solutions of differential equations continuously into other solutions. This property can be used for the observability analysis of infinite-dimensional systems with input and output. In this contribution,…
We consider a system of differential equations and obtain its solutions with exponential asymptotics and analyticity with respect to the spectral parameter. Solutions of such type have importance in studying spectral properties of…
In this paper we consider the model semilinear Neumann system $$\left\{ \begin{array}{lll} -\Delta u+a(x)u=\lambda c(x) F_u(u,v)& {\rm in} & \Omega,\\ -\Delta v+b(x)v=\lambda c(x) F_v(u,v)& {\rm in} & \Omega,\\ \frac{\partial u}{\partial…
Systems of nonlinear ordinary differential equations are constructed, for which the general solution is algebraically expressed in terms of a finite number of particular solutions. Expressions of that type are called the nonlinear…
In this paper we mainly study the existence and the form of entire solutions with finite order for the following system of Fermat-type difference and partial differential-difference equations $$\begin{cases} f_1(z)^2+(\Delta_cf_2(z))^2=1\cr…
A novel approach is introduced for deriving exact solutions to nonlinear systems of ordinary differential equations. This method consists of four parts. In the initial part, the examined nonlinear differential equation system is transformed…
The purpose of this paper is to propose a semi-analytical technique convenient for numerical approximation of solutions of the initial value problem for $p$-dimensional delayed and neutral differential systems with constant, proportional…
We construct a new family of entire solutions for the nonlinear Schr\"odinger equation \begin{align*} \begin{cases} -\Delta u+ V(y ) u = u^p, \quad u>0, \quad \text{in}~ \mathbb{R}^N, \\[2mm] u \in H^1(\mathbb{R}^N), \end{cases}…
In this study, a recursive solution technique in conjunction with generalized integrating factors is presented and applied to address first and second order linear differential equations. This approach demonstrates practical utility in…
In this paper, we classify the solution of the following mixed-order conformally invariant system with coupled nonlinearity in $ \mathbb{R}^4$: \begin{equation}\left\{ \begin{aligned} & -\Delta u(x) = u^{p_1}(x) e^{q_1v(x)}, \quad x\in…
This work considers special types of interval linear systems - overdetermined systems. Simply said these systems have more equations than variables. The solution set of an interval linear system is a collection of all solutions of all…
This paper is the first in a series of papers which will address, on a case by case basis, the special cases of the following rational system in the plane, labeled system #11. $$x_{n+1}=\frac{\alpha_{1}}{A_{1}+y_{n}},\quad…
Modelling real world systems frequently requires the solution of systems of nonlinear equations. A number of approaches have been suggested and developed for this computational problem. However, it is also possible to attempt solutions…