Related papers: A generalization of Sturm's comparison theorem
The purpose of this paper is to investigate the role that the continuous-time generalised Riccati equation plays within the context of singular linear-quadratic optimal control. This equation has been defined following the analogy with the…
A three-dimensional Riccati differential equation of complex quaternion-valued functions is studied. Many properties similar to those of the ordinary differential Riccati equation such that linearization and Picard theorem are obtained. Lie…
An indefinite stochastic Riccati Equation is a matrix-valued, highly nonlinear backward stochastic differential equation together with an algebraic, matrix positive definiteness constraint. We introduce a new approach to solve a class of…
Applying the resolution-scale relativity principle to develop a mechanics of non-differentiable dynamical paths, we find that, in one dimension, stationary motion corresponds to an Ito process driven by the solutions of a Riccati equation.…
The geometric theory of Lie systems is used to establish integrability conditions for several systems of differential equations, in particular some Riccati equations and Ermakov systems. Many different integrability criteria in the…
In this paper we present a numerical scheme for the resolution of matrix Riccati equation, usualy used in control problems. The scheme is unconditionnaly stable and the solution is definite positive at each time step of the resolution. We…
In this work, a generalization of the well known Bernoulli inequality is obtained by using the theory of discrete fractional calculus. As far as we know our approach is novel.
The notion of viscosity solutions of scalar fully nonlinear partial differential equations of second order provides a framework in which startling comparison and uniqueness theorems, existence theorems, and theorems about continuous…
Discrete algebraic Riccati equations and their fixed points are well understood and arise in a variety of applications, however, the time-varying equations have not yet been fully explored in the literature. In this article we provide a…
A spectral decomposition method is used to obtain solutions to a class of nonlinear differential equations. We extend this approach to the analysis of the fractional form of these equations and demonstrate the method by applying it to the…
A global approximation method of Nystr\"om type is explored for the numerical solution of a class of nonlinear integral equations of the second kind. The cases of smooth and weakly singular kernels are both considered. In the first…
The systems of differential equations whose solutions coincide with Bethe ansatz solutions of generalized Gaudin models are constructed. These equations we call the {\it generalized spectral Riccati equations}, because the simplest equation…
We consider the Ricatti equation in the context of population dynamics, quantum scattering and a more general context. We examine some exactly solvable cases of real life interest.
We present a generic functional inequality on Riemannian manifolds, both in additive and multiplicative forms, that produces well known and genuinely new Hardy-type inequalities. For the additive version, we introduce Riccati pairs that…
The concept of turnpike connects the solution of long but finite time horizon optimal control problems with steady state optimal controls. A key ingredient of the analysis of the turnpike is the linear quadratic regulator problem and the…
A general organizing principle is proposed that can be used to derive the equations of motion describing the near-equilibrium dynamics of causal and thermodynamically stable relativistic systems. The latter are found to display some new…
We present a matrix method for obtaining new classes of exact solutions for Einstein's equations representing static perfect fluid spheres. By means of a matrix transformation, we reduce Einstein's equations to two independent Riccati type…
We consider properties of binomial series $\sum_{n=0}^\infty a_n z^{\underline{n}}$, where $z^{\underline{n}}=z(z-1)\cdots(z-n+1)$ and the convergence of binomial series in the complex domain. The order of growth of entire and meromorphic…
It is shown that the expressions for the tangential pressure, the anisotropy factor and the radial pressure in the Einstein equations may serve as generating functions for stellar models. The latter can incorporate an equation of state when…
We prove a simple inequality for a sum of squares of norms of two vectors in an inner product space. Next, using this inequality we derive the so--called "reverse uncertainty relation" and analyze its properties.