Related papers: Comparison criterion for second order Riccati equa…
We obtain explicit formulas for the solutions of the system of second-order difference equations of the form $x_{n+ 1} = \frac{x_n y_{n-1}}{y_n (a_n + b_n x_n y_{n - 1})}, \quad y_{n+1} = \frac{x_{n - 1} y_n}{x_n (c_n+d_n x_{n-1} y_n)}$,…
A class of fourth--order neutral type difference equations with quasidifferences and deviating arguments is considered. Our approach is based on studying the considered equation as a system of a four--dimensional difference system. The…
For a second-order elliptic equation in divergence form we investigate conditions on the coefficients which imply that all solutions are Lipschitz continuous or differentiable at a given point. We assume the coefficients have modulus of…
We consider difference equations with several non-monotone deviating arguments and nonnegative coefficients. The deviations (delays and advances) are, generally, unbounded. Sufficient oscillation conditions are obtained in an explicit…
We present two algorithms for computing what we call the absolute factorization of a difference operator. We also give an algorithm to solve third order difference equations in terms of second order equations, together with applications to…
Lie symmetry analysis is one of the powerful tools to analyze nonlinear ordinary differential equations. We review the effectiveness of this method in terms of various symmetries. We present the method of deriving Lie point symmetries,…
Mixed superposition rules, i.e., functions describing the general solution of a system of first-order differential equations in terms of a generic family of particular solutions of first-order systems and some constants, are studied. The…
Ten new exact solutions of the Riccati equation $dy/dx=a(x)+b(x)y+c(x)y^{2}$ are presented. The solutions are obtained by assuming certain relations among the coefficients $a(x)$, $b(x)$ and $c(x)$ of the Riccati equation, in the form of…
In this paper we study the existence of continuous solutions and their constructions for a second order iterative functional equation, which involves iterate of the unknown function and a nonlinear term. Imposing Lipschitz conditions to…
In this work we investigate the existence of solutions, their uniqueness and finally dependence on parameters for solutions of second order neutral nonlinear difference equations. The main tool which we apply is Darbo fixed point theorem.
Logicians and philosophers of science have proposed various formal criteria for theoretical equivalence. In this paper, we examine two such proposals: definitional equivalence and categorical equivalence. In order to show precisely how…
The paper proposes new second-order accuracy metrics for scoring or rating models, which show the target preference of the model, it is better to diagnose good objects or better to diagnose bad ones for a constant generally accepted…
In this paper we develop some group theoretical methods which are shown to be very useful for a better understanding of the properties of the Riccati equation and we discuss some of its integrability conditions from a group theoretical…
In this paper, we, for the first time, establish two comparison theorems for multi-dimensional backward stochastic differential equations with jumps. Our approach is novel and completely different from the existing results for…
In this paper, we investigate the existence of multiple periodic solutions for two classes of nonlinear difference systems involving $(\phi_1,\phi_2)$-Laplacian. First, by using an important critical point theorem due to B. Ricceri, we…
This paper deals with the comparison of two common types of equivalence groups of differential equations, and this gives rise to a number of results presented in the form of theorems. It is shown in particular that one type can be…
The bivariate difference field provides an algebraic framework for a sequence satisfying a recurrence of order two. Based on this, we focus on sequences satisfying a recurrence of higher order, and consider the multivariate difference…
Consider the first-order linear differential equation with several retarded arguments $$ x^{\prime}(t)+\sum\limits_{i=1}^{m}p_{i}(t)x(\tau_{i}(t))=0,\;\;\;t\geq t_{0}, $$ where the functions $p_{i},\tau_{i}\in…
We present a method to obtain symmetries for second-order systems of ordinary difference equations and how to use them to reduce the order. We also introduce a technique of finding conservation laws for such systems.
This paper introduces a generalization of the well-known Riccati recursion for solving the discrete-time equality-constrained linear quadratic optimal control problem. The recursion can be used to compute the solutions as well as optimal…