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Algebraic Riccati equations are encountered in many applications of control and engineering problems, e.g., LQG problems and $H^\infty$ control theory. In this work, we study the properties of one type of discrete-time algebraic Riccati…
This paper deals with reduction of non-homogeneous linear systems of first order operator equations with constant coefficients. An equivalent reduced system, consisting of higher order linear operator equations having only one variable and…
The first part of this paper is devoted to an analysis of moment problems in R^n with supports contained in a closed set defined by finitely many polynomial inequalities. The second part of the paper uses the representation results of…
We establish the uniqueness of the higher radial bound state solutions of $$ \Delta u +f(u)=0,\quad x\in \RR^n. \leqno(P) $$ We assume that the nonlinearity $f\in C(-\infty,\infty)$ is an odd function satisfying some convexity and growth…
In this paper we introduce a very general setting dealing with the superposition of operators of any positive order and provide a systematic study of them. We also provide examples and counterexamples, as well as characterizing properties…
This paper analyzes the structure of the set of positive solutions of a class of one-dimensional superlinear indefinite bvp's. It is a paradigm of how mathematical analysis aids the numerical study of a problem, whereas simultaneously its…
Various types of stabilizing controls lead to a deterministic difference equation with the following property: once the initial value is positive, the solution tends to the unique positive equilibrium. Introducing additive perturbations can…
We consider the decidability and complexity of the Ultimate Positivity Problem, which asks whether all but finitely many terms of a given rational linear recurrence sequence (LRS) are positive. Using lower bounds in Diophantine…
Assuming $B_{R}$ is a ball in $\mathbb R^{N}$, we analyze the positive solutions of the problem \[ \begin{cases} -\Delta u+u= |u|^{p-2}u, &\text{ in } B_{R},\newline \partial_{\nu}u=0,&\text{ on } \partial B_{R}, \end{cases} \] that branch…
We present sufficient conditions for the existence of positive solutions for a class of fractional singular boundary value problems in presence of Caputo fractional derivative. Further, the nonlinearity involved has singularity with respect…
Motivated by satisfiability of constraints with function symbols, we consider numerical inequalities on non-negative integers. The constraints we consider are a conjunction of a linear system Ax = b and a conjunction of (non-)convex…
The idea of monotonicity (or positive-definiteness in the linear case) is shown to be the central theme of the solution theories associated with problems of mathematical physics. A "grand unified" setting is surveyed covering a…
There are four variants of passive, linear time-invariant systems, described by rational functions: Continuous or Discrete time, Positive or Bounded real. By introducing a quadratic matrix inequality formulation, we present a unifying…
We present an imperative object calculus where types are annotated with qualifiers for aliasing and mutation control. There are two key novelties with respect to similar proposals. First, the type system is very expressive. Notably, it…
Using the sub-supersolution method we study the existence of positive solutions for the anisotropic problem \begin{equation} -\sum_{i=1}^N\frac{\partial}{\partial x_i}\left( \left|\frac{\partial u}{\partial x_i}\right|^{p_i-2}\frac{\partial…
In this paper, we study a class of double phase systems which contain the singular and mixed nonlinear terms. Unlike the single equation, the mixed nonlinear terms make the problem more complicate. The geometry of the fibering mapping has…
In this paper, we provide an affirmative answer to the {\it conjecture A} for bounded simple rotationally symmetric domains $\Omega\subset \mathbb{R}^n(n\geq 3)$ along $x_n$ axis. Precisely, we use a new simple argument to study the…
The first goal of this paper is to establish the existence of a positive solution for the singular boundary value problem (1.1), where $\mathcal{B}$ is a general boundary operator of Dirichlet, Neumann or Robin type, either classical or…
The dynamical behavior of switched affine systems is known to be more intricate than that of the well-studied switched linear systems, essentially due to the existence of distinct equilibrium points for each subsystem. First, under…
Characterizing in a constructive way the set of real functions whose Fourier transforms are positive appears to be yet an open problem. Some sufficient conditions are known but they are far from being exhaustive. We propose two constructive…