Related papers: Principal eigenvalue and maximum principle for coo…
We establish necessary and sufficient conditions for the realization of mapping schemata as post-critically finite polynomials, or more generally, as post-critically finite polynomial maps from a finite union of copies of the complex…
A certain class of integrable hydrodynamic type systems with three independent and N dependent variables is considered. We choose the existence of a pseudopotential as a criterion of integrability. It turns out that the class of integrable…
Supertropical matrix theory was investigated in [6], whose terminology we follow. In this work we investigate eigenvalues, characteristic polynomials and coefficients of characteristic polynomials of supertropical matrices and their powers,…
This work is concerned with the identification problem for what we call the perturbation term or error term in a parabolic partial differential equation, through its approximate periodic solutions. The observation is made over a subregion…
In this paper we establish existence, nonexitence and regularity of positive solutions for a class of singular quasilinear elliptic systems subject to (super-) homogeneous condition. The approach is based on sub-supersolution methods for…
The purpose of this short note is to show how it is possible to combine existing results in the literature to get the unique continuation from sets of positive measure for time dependent parabolic equations with Lipschitz principal part and…
Parametric linear systems are linear systems of equations in which some symbolic parameters, that is, symbols that are not considered to be candidates for elimination or solution in the course of analyzing the problem, appear in the…
We introduce a new method for proving the nonexistence of positive supersolutions of elliptic inequalities in unbounded domains of $\mathbb{R}^n$. The simplicity and robustness of our maximum principle-based argument provides for its…
We establish via variational methods the existence of a standing wave together with an estimate on the convergence to its asymptotic states for a bistable system of partial differential equations on a periodic domain. The main tool is a…
The goal of this paper is to provide a qualitative analysis of the optimisation of space-time periodic principal eigenvalues. Namely, considering a fixed time horizon $T$ and the $d$-dimensional torus $\mathbb{T}^d$, let, for any $m\in…
This paper aims to explore the relationship between maximum principle and dynamic programming principle for stochastic recursive control problem with random coefficients. Under certain regular conditions for the coefficients, the…
We study a class of overdetermined algebraic systems of equations. We prove that the number of distinct solutions equals to the maximal possible if and only if certain matrices are commuting and semisimple. This gives a characterization of…
Optimal approximation and optimal interpolation problems on the classes of periodic functions that are determined by restrictions on several higher derivatives of the functions are solved.
The goal of this note is to give the unified approach to the solutions of a class of isoperimetric problems by relating them to the exterior differential systems studied by R.~Bryant and P.~Griffiths. In this note we list several classical…
Motivated by the study of systems of higher order boundary value problems with functional boundary conditions, we discuss, by topological methods, the solvability of a fairly general class of systems of perturbed Hammerstein integral…
This paper is devoted to the homogenization of weakly coupled cooperative parabolic systems in strong convection regime with purely periodic coefficients. Our approach is to factor out oscillations from the solution via principal…
We prove the well posedness of a class of non linear and non local mixed hyperbolic-parabolic systems in bounded domains, with Dirichlet boundary conditions. In view of control problems, stability estimates on the dependence of solutions on…
We investigate the Courr\`{e}ge theorem in the context of linear operators $A$ that satisfy the positive maximum principle on a space of continuous functions over a symmetric space. Applications are given to Feller--Markov processes. We…
We study the existence of principal eigenvalues and principal eigenfunctions for weighted eigenvalue problems of the form: \begin{equation*} - \mbox{div} ( L (x) |\nabla u|^{p-2} \nabla u ) = \lambda K(x) |u|^{p-2} u \hspace{.1cm} \mbox {…
We consider parabolic equations with mixed boundary conditions and domain inhomogeneities supported on a lower dimensional hypersurface, enforcing a jump in the conormal derivative. Only minimal regularity assumptions on the domain and the…