相关论文: Existence and uniqueness of solutions for Leontief…
We study the set of intrinsic singularities of flat affine systems with $n-1$ controls and $n$ states using the notion of Lie-B\"acklund atlas, previously introduced by the authors. For this purpose, we prove two easily computable…
We consider a class of finite Markov moment problems with arbitrary number of positive and negative branches. We show criteria for the existence and uniqueness of solutions, and we characterize in detail the non-unique solution families.…
The purpose of this paper is to develop a general existence theory for constrained minimization problems for functionals defined on function spaces on metric measure spaces $(\mathcal M, d, \mu)$. We apply this theory to functionals defined…
Given a full column rank matrix $A \in \mathbb{R}^{m\times n}$ ($m\geq n$), we consider a special class of linear systems of the form $A^\top Ax=A^\top b+c$ with $x, c \in \mathbb{R}^{n}$ and $b \in \mathbb{R}^{m}$. The occurrence of $c$ in…
In this paper we study the existence of multiple nontrivial positive weak solutions to the following system of problems. \begin{align*} \begin{split} -\Delta_{p}u-\Delta_q u &= \lambda f(x)|u|^{r-2}u+\nu\frac{1-\alpha}{2-\alpha-\beta}h(x)…
In this paper, we present a general framework for constructively proving the existence and of stationary localized solutions, spatially periodic solutions, and branches of spatially periodic solutions in the 1D Thomas model. Specifically,…
The accuracy of probability distributions inferred using machine-learning algorithms heavily depends on data availability and quality. In practical applications it is therefore fundamental to investigate the robustness of a statistical…
This paper deals with the one-dimensional formulation of Hughes model for pedestrian flows in the setting of entropy solutions, which authorizes non-classical shocks at the location of the so-called turning curve. We consider linear cost…
We investigate the multiplicity and uniqueness of positive solutions for the superlinear singular $(p,q)$-Laplacian equation \begin{eqnarray*} \begin{cases} -\Delta_p u-\Delta_q u+a(x)u^{p-1}+b(x)u^{q-1}=f(x)u^{-\gamma}+\lambda…
This article is interested in internality to the constants of systems of autonomous algebraic ordinary differential equations. Roughly, this means determining when can all solutions of such a system be written as a rational function of…
Many physical systems--from mechanical lattices and electrical circuits to biological tissues and architected metamaterials--can be understood as networks transmitting physical quantities. We present a unified mathematical framework for…
This paper deals with the non-uniqueness of the solutions of an analysis-Lasso regularization. Most of previous works in this area is concerned with the case where the solution set is a singleton, or to derive guarantees to enforce…
An asymptotic method for finding instabilities of arbitrary $d$-dimensional large-amplitude patterns in a wide class of reaction-diffusion systems is presented. The complete stability analysis of 2- and 3-dimensional localized patterns is…
We examine a family of 3-point mappings that include mappings solvable through linearization. The different origins of mappings of this type are examined: projective equations and Gambier systems. The integrable cases are obtained through…
We investigate uniqueness of solutions to certain classes of elliptic and parabolic equations posed on metric graphs. In particular, we address the linear Schr\"odinger equation with a potential, and the heat equation with a variable…
We study the systems of ordinary differential equations which are implicit with respect to the higher derivatives, appearing in the linear form, and their solutions near the singular points. The invertibility of the higher derivatives…
In this work, we study the mathematical analysis of a coupled system of two reaction-diffusion-advection equations and Danckwerts boundary conditions, which models the interaction between a microbial population (e.g., bacterias) and a…
We consider linear elimination of variables in steady state equations of a chemical reaction network. Particular subsets of variables corresponding to sets of so-called reactant-noninteracting species, are introduced. The steady state…
We investigate the existence, non-existence, uniqueness, and multiplicity of positive solutions to the following problem: \begin{align}\label{P} \left\{ \begin{array}{l} D_{0+}^\alpha u + h(t)f(u) = 0, \quad 0<t<1, \\[1ex] u(0)=u(1)=0,…
This paper is concerned with a nonlinear fractional Sch\"ordinger system in $\mathbb{{R}}$ with intraspecies interactions $a_{i}>0 \ (i=1,2)$ and interspecies interactions $\beta \in\mathbb{{R}}$. We study this system by solving an…