Related papers: Periodic solutions of quaternionic Riccati equatio…
In this paper we study properties of regular solutions of quaternionic Riccati equations. The obtained results we use for study of the asymptotic behavior of solutions of two first-order linear quaternionic ordinary differential equations.
A quaternionic partial differential equation is shown to be a generalisation of the Riccati ordinary differential equation and its relationship with the Schrodinger equation is established. Various approaches to the problem of finding…
In this paper, we study the existence and uniqueness of periodic solutions of the differential equation of the form . Here, we obtain some sufficient conditions which guarantee the existence of periodic solutions. This equation is a quite…
The purpose of this paper is to study the existence of (weak) periodic solutions for nonlocal fractional equations with periodic boundary conditions. These equations have a variational structure and, by applying a critical point result…
Some global existence criteria for quaternionic Riccati equations are established. Two of them are used to prove a completely non conjugation theorem for solutions of linear systems of ordinary differential equations.
We propose a new algorithm for a broad class of periodic time-varying Stochastic Game-Theoretic Riccati Differential Equations arising in Zero-Sum Linear-Quadratic Stochastic Differential Games. The algorithm is constructed via dual-layer…
Cubic and quartic non-autonomous differential equations with continuous piecewise linear coefficients are considered. The main concern is to find the maximum possible multiplicity of periodic solutions. For many classes, we show that the…
This work is devoted to the study of the existence and periodicity of solutions of initial differential problems, paying special attention to the explicit computation of the period. These problems are also connected with some particular…
In this paper we present some results related to the problem of finding periodic representations for algebraic numbers. In particular, we analyze the problem for cubic irrationalities. We show an interesting relationship between 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 article, we investigate the existence and properties of time-periodic solutions for damped evolutionary partial differential equations subject to periodic forcing. Particular emphasis is placed on configurations where the energy…
This paper is concerned with the problem of existence of periodic solutions for perturbative Carath\'{e}odory differential equations. The main result provides sufficient conditions on the averaged equation that guarantee the existence of…
A simple non-autonomous scalar differential equation with delay, exponential decay, nonlinear negative feedback and a periodic multiplicative coefficient is considered. It is shown that stable slowly oscillating periodic solutions with the…
We study a one-dimensional ordinary differential equation modelling optical conveyor belts, showing in particular cases of physical interest that periodic solutions exist. Moreover, under rather general assumptions it is proved that the set…
A comprehensive analysis of the morphology of the solution space for a special type of quadratic quaternion equation is presented. This equation, which arises in a surface construction problem, incorporates linear terms in a quaternion…
We prove the existence of periodic solutions in a class of nonlinear partial differential equations, including the nonlinear Schroedinger equation, the nonlinear wave equation, and the nonlinear beam equation, in higher dimension. Our…
We study time-periodic solutions for the cubic wave equation on an interval with Dirichlet boundary conditions. We begin by following the perturbative construction of Vernov and Khrustalev and provide a rigorous derivation of the…
We show that a problem on minimal periods of solutions of Lipschitz functional differential equations is closely related to the unique solvability of the periodic problem for linear functional differential equations. Sharp bounds for…
We study necessary conditions and sufficient conditions for the existence of local-in-time solutions of the Cauchy problem for superlinear fractional parabolic equations. Our conditions are sharp and clarify the relationship between the…
In this paper we investigate the properties of the set of T-periodic solutions of semi-explicit parametrized Differential-Algebraic Equations with non-autonomous constraints of a particular type. We provide simple, degree theoretic…