Related papers: Global solvability criteria for quaternionic Ricca…
This paper presents a new interpretation of the Lyapunov and Riccati equations from the perspective of positive system theory. We show it is possible to construct positive systems related to these equations, and then certain conclusions --…
In this paper we study a mixed problem for the nonlinear Schr\"odinger equation globally that have a nonlinear adding, in which the coefficient is a generalized function. Here is proved a global solvability theorem of the considered problem…
In this paper, we deal with two logarithmic fourth order differential equations: the extended one-dimensional DLSS equation and its multi-dimensional analog. We show the global existence of solution in critical spaces, its convergence to…
We consider the question of diagonal Riccati stability for a pair of real matrices A, B. A necessary and sufficient condition for diagonal Riccati stability is derived and applications of this to two distinct cases are presented. We also…
Using the Chiellini condition for integrability we derive explicit solutions for a generalized system of Riccati equations $\ddot{x}+\alpha x^{2n+1}\dot{x}+x^{4n+3}=0$ by reduction to the first-order Abel equation assuming the parameter…
In this paper we establish three global in time results for two fourth order nonlinear parabolic equations. The first of such equations involves the Hessian and appears in epitaxial growth. For such equation we give conditions ensuring the…
We study rigidity/flexibility properties of global solutions to the thin obstacle problem. For solutions with bounded positive sets, we give a classification in terms of their expansions at infinity. For solutions with bounded contact sets,…
We consider the algebraic Riccati equation for which the four coefficient matrices form an M-matrix K. When K is a nonsingular M-matrix or an irreducible singular M-matrix, the Riccati equation is known to have a minimal nonnegative…
A general formalism to solve nonlinear differential equations is given. Solutions are found and reduced to those of second order nonlinear differential equations in one variable. The approach is uniformized in the geometry and solves…
We show that any global solution to the special Lagrangian equations with the phase larger than a critical value must be quadratic.
A class of two-dimensional systems of second-order ordinary differential equations is identified in which a system requires fewer Lie point symmetries than required to solve it. The procedure distinguishes among those which are…
We are interested in the cubic Dirac equation in two space dimensions. We establish the small data global existence and sharp pointwise decay results for general cubic nonlinearities without additional structure. We also prove the…
We consider matrix Riccati inequality arising in the theory of absolute stability, $H_\infty$ control problem, $LQ$ problem, and optimal estimation problem. In the case of sign definite frequency domain function, the solvability of Riccati…
We introduce the notion of Differential Sequences of ordinary differential equations. This is motivated by related studies based on evolution partial differential equations. We discuss the Riccati Sequence in terms of symmetry analysis,…
An algebraic Riccati equation for linear operators is studied, which arises in systems theory. For the case that all involved operators are unbounded, the existence of infinitely many selfadjoint solutions is shown. To this end, invariant…
The differential equations with piecewise constant argument (DEPCAs, for short) is a class of hybrid dynamical systems (combining continuous and discrete). In this paper, under the assumption that the nonlinear term is partially unbounded,…
We use the Riccati equation method with other ones to establish new oscillation and interval oscillation criteria for linear matrix Hamiltonian systems. We investigate the oscillation problem for linear matrix Hamiltonian systems in a new…
In this study, the Riccati equation is resolved using the generalized recursive integrating factor method. By applying a non-linear transformation to the dependent variable $y(x)$ of the Riccati equation, a second-order linear differential…
A recent problem [B. Gardas, J. Math. Phys. 52, 042104 (2011)] concerning an antilinear solution of the Riccati equation is solved. We also exemplify that a simplification of the Riccati equation, even under reasonable assumptions, can lead…
We extend the criterion of Kawatani and Okawa for indecomposability of the derived category of a smooth projective variety to arbitrary schemes. For relative schemes, we also give a criterion for the nonexistence of semiorthogonal…