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We consider some multivariate rational functions which have (or are conjectured to have) only positive coefficients in their series expansion. We consider an operator that preserves positivity of series coefficients, and apply the inverse…
The solution to systems of moment differential equations of the form $z\partial_my=(zA+B)y$ are provided, for a matrix $B$ with general good spectrum. Existence and convergence of Floquet-type solutions is studied. A generalized definition…
In this paper, some useful necessary and sufficient conditions for the unique solution of the generalized absolute value equation (GAVE) $Ax-B|x|=b$ with $A, B\in \mathbb{R}^{n\times n}$ from the optimization field are first presented,…
We present a convenient notation for positive/negative-conditional equations. The idea is to merge rules specifying the same function by using case-, if-, match-, and let-expressions. Based on the presented macro-rule-construct,…
The problem of inverting a system in presence of a series-defined output is analyzed. Inverse models are derived that consist of a set of algebraic equations. The inversion is performed explicitly for an output trajectory functional, which…
Linear Dynamical Systems, both discrete and continuous, are invaluable mathematical models in a plethora of applications such the verification of probabilistic systems, model checking, computational biology, cyber-physical systems, and…
We deal with the existence of positive solutions for a two-point boundary value problem associated with the nonlinear second order equation $u''+a(x)g(u)=0$. The weight $a(x)$ is allowed to change its sign. We assume that the function…
We study initial value problems having dynamics ruled by discontinuous ordinary differential equations with the property of possessing a unique solution. We identify a precise class of such systems that we call solvable intitial value…
Over an algebraically closed field of positive characteristic, there exist rational functions with only one critical point. We give an elementary characterization of these functions in terms of their continued fraction expansions. Then we…
A recurrence relations for sums of powers of complex functions can be written as a system of linear equation AX=B. Using properties of determinant and Cramer's rule for solving systems of linear equation, this paper presents an absolutely…
We consider the iterative solution of large linear systems of equations in which the coefficient matrix is the sum of two terms, a sparse matrix $A$ and a possibly dense, rank deficient matrix of the form $\gamma UU^T$, where $\gamma > 0$…
We establish the existence of strong solutions to a class of nonlinear strongly coupled and uniform elliptic systems consisting of more than two equations. The existence of of nontrivial and non constant solutions (or pattern formations)…
A solution of linear systems of equations Ax=b and Ax=0 is a vital part of many computational packages. This paper presents a novel formulation based on the projective extension of the Euclidean space using the outer product (extended…
We study the existence of non-zero positive solutions of a class of systems of differential equations driven by fractional powers of the Laplacian. Our approach is based on the notion of fixed point index, and allows us to deal with…
We discuss linear autonomous evolution equations on function spaces which have the property that a positive initial value leads to a solution which initially changes sign, but then becomes - and stays - positive again for sufficiently large…
This paper is devoted to derive some necessary and suficient conditions for the existence of positive solutions to a singular second order system of dynamic equations with Dirichlet boundary conditions. The results are obtained by employing…
We provide new results on the existence of nonzero positive weak solutions for a class of second order elliptic systems. Our approach relies on a combined use of iterative techniques and classical fixed point index. Some examples are…
Let $a, b\in \mathbb{N}$ be relatively prime. Previous work showed that exactly one of the two equations $ax + by = (a-1)(b-1)/2$ and $ax + by + 1 = (a-1)(b-1)/2$ has a nonnegative, integral solution; furthermore, the solution is unique.…
In this article we find the equivalent conditions to assure the existence and uniqueness of positive solutions to semilinear elliptic equations wih double power nonlinearities. As a bonus, we give a simpler proof of our former result that…
Bilinear systems of equations are defined, motivated and analyzed for solvability. Elementary structure is mentioned and it is shown that all solutions may be obtained as rank one completions of a linear matrix polynomial derived from…