Related papers: A stochastic Schauder-Tychonoff type theorem and i…

In this paper we develop the $l_p$-theory of space-time stochastic difference equations which can be considered as a discrete counterpart of N.V. Krylov's $L_p$-theory of stochastic partial differential equations. We also prove a…

We prove a scattering result near certain steady states for a Hartree equation for a random field. This equation describes the evolution of a system of infinitely many particles. It is an analogous formulation of the usual Hartree equation…

The results of the author and Gess [27] develop a robust well-posedness theory for a broad class of conservative stochastic PDEs, with both probabilistically stationary and non-stationary Stratonovich noise, and with irregular noise…

We consider the Cauchy problem for the defocusing stochastic nonlinear Schr\"odinger equations (SNLS) with an additive noise in the mass-critical and energy-critical settings. By adapting the probabilistic perturbation argument employed in…

We consider the long-time behavior of an explicit tamed exponential Euler scheme applied to a class of parabolic semilinear stochastic partial differential equations driven by additive noise, under a one-sided Lipschitz continuity…

The objective of this paper is to introduce and study a complicated nonlinear system, called coupled variational-hemivariational inequalities, which is described by a highly nonlinear coupled system of inequalities on Banach spaces. We…

Retarded stochastic differential equations (SDEs) constitute a large collection of systems arising in various real-life applications. Most of the existing results make crucial use of dissipative conditions. Dealing with "pure delay" systems…

We study nonlinear stationary Kolmogorov equations with degenerate diffusion matrices and discontinuous coefficients. The existence of a solution is proved. We propose a new approach based on an integral condition with Lyapunov functions…

We study a class of stochastic differential equations with non-Lipschitzian coefficients.A unique strong solution is obtained and a large deviation principle of Freidln-Wentzell type has been established.

We obtain global and local theorems on the existence of invariant manifolds for perturbations of non autonomous linear differential equations assuming a very general form of dichotomic behavior for the linear equation. Besides some new…

We establish the local well-posedness for a new nonlinearly dispersive wave equation and we show that the equation has solutions that exist for indefinite times as well as solutions which blowup in finite times. Furthermore, we derive an…

We consider reaction-diffusion equations that are stochastically forced by a small multiplicative noise term. We show that spectrally stable travelling wave solutions to the deterministic system retain their orbital stability if the…

In the paper we study a measure version of the evolutionary nonlinear Boltzmann-type equation in which we admit a random number of collisions of particles. We consider first a stationary model and use two methods to find its fixed points:…

We develop the existence, uniqueness, continuity, stability, and scattering theory for energy-critical nonlinear Schr\"odinger equations in dimensions $n \geq 3$, for solutions which have large, but finite, energy and large, but finite,…

In this paper I prove the existence of a positive stationary solution for a generic quasilinear model of structured population. The existence is proved using Schauder's fixed point theorem. The theorem is applied to a hierarchically…

In this paper, we used some theorems of fixed point for studying the results of existence and uniqueness for Hilfer-Hadamard-Type fractional differential equations, \[_{H}D^{\alpha,\beta}x(t)+f(t,x(t))=0, \hbox{ on the interval } J:=(1,e]\]…

We prove a Stroock-Varadhan's type support theorem for a stochastic partial differential equation (SPDE) on the real line with a noise term driven by a cylindrical Wiener process on $L_2 (\mathbb{R})$. The main ingredients of the proof are…

This paper extends deterministic notions of Strong Stability Preservation (SSP) to the stochastic setting, enabling nonlinearly stable numerical solutions to stochastic differential equations (SDEs) and stochastic partial differential…

In this paper, we study the existence of random periodic solutions for nonlinear stochastic differential equations with additive white noise. We extend the input-to-state characteristic operator of the system to the non-autonomous…

Nonuniform ellipticity is a classical topic in the theory of partial differential equations. While several results in regularity theory have been adding up over decades, many basic issues, as for instance the validity of Schauder theory and…