Related papers: Measure Differential Equation with a Nonlinear Gro…
We study approximation of non-autonomous linear differential equations with variable delay over infinite intervals. We use piecewise constant argument to obtain a corresponding discrete difference equation. The study of numerical…
We establish several delay-independent criteria for the existence and stability of positive periodic solutions of n-dimensional nonautonomous functional differential equation by several fixed point theorems. Examples from positive and…
We establish the rectifiability of measures satisfying a linear PDE constraint. The obtained rectifiability dimensions are optimal for many usual PDE operators, including all first-order systems and all second-order scalar operators. In…
The branching methods developed are effective methods to solve some semi linear PDEs and are shown numerically to be able to solve some full non linear PDEs. These methods are however restricted to some small coefficients in the PDE and…
Deriving the time evolution of a distribution of probability (or a probability density matrix) is a problem encountered frequently in a variety of situations: for physical time, it could be a kinetic reaction study, while identifying time…
In this paper we determine the exact rate of growth of the solution of a deterministic delay differential equation in which the delayed term is regularly varying at infinity and dominates, and determine criteria to characterise this…
We consider backward stochastic differential equations (BSDE) with nonlinear generators typically of quadratic growth in the control variable. A measure solution of such a BSDE will be understood as a probability measure under which the…
Solutions of Rough Differential Equations (RDE) may be defined as paths whose increments are close to an approximation of the associated flow. They are constructed through a discrete scheme using a non-linear sewing lemma. In this article,…
We introduce a new formulation for differential equation describing dynamics of measures on an Euclidean space, that we call Measure Differential Equations with sources. They mix two different phenomena: on one side, a transport-type term,…
We introduce a new approach for designing numerical schemes for stochastic differential equations (SDEs). The approach, which we have called direction and norm decomposition method, proposes to approximate the required solution $X_t$ by…
In this paper, we prove existence and uniqueness of measure solutions for the Cauchy problem associated to the (vectorial) continuity equation with a non-local flow. We also give a stability result with respect to various parameters.
Stability and boundedness analysis for vector nonlinear systems with variable delays and coefficients remains challenging due to the conservatism of existing methods. Moreover, estimates of the transient behavior of solution norms remain…
The existence of numerical solutions to a fourth order singular boundary value problem arising in the theory of epitaxial growth is studied. An iterative numerical method is applied on a second order nonlinear singular boundary value…
We prove the existence and uniqueness of measure solutions to the conservative renewal equation and analyze their long time behavior. The solutions are built by using a duality approach. This construction is well suited to apply the…
This paper provides a formal econometric framework behind the newly developed difference-in-discontinuities design (DiDC). Despite its increasing use in applied research, there are currently limited studies of its properties. We formalize…
The aim of this short note is twofold. First, we give a sketch of the proof of a recent result proved by the authors in the paper [Colombo, Crippa, and Spirito, Calc. Var. Partial Differential Equations 2015] concerning existence and…
This paper focuses on explicit approximations for nonlinear stochastic delay differential equations (SDDEs). Under the weakly local Lipschitz and some suitable conditions, a generic truncated Euler-Maruyama (TEM) scheme for SDDEs is…
In this paper, the development of a mathematical method is presented to explore spatially non-uniform phases with no long-range order in mathematical models of first order phase transitions. We use essential results regarding the…
We establish the existence of positive solutions for a nonlinear elliptic Dirichlet problem in dimension $N$ involving the $N$-Laplacian. The nonlinearity considered depends on the gradient of the unknown function and an exponential term.…
We study parametric double phase problems involving superlinear nonlinearities with a growth that need not necessarily be polynomial. Based on truncation and comparison methods the existence of two constant sign solutions is shown provided…