Related papers: Infinite first order differential systems with non…
We prove the global strong solvability of a quasilinear initial-boundary value problem with fractional time derivative of order less than one. Such problems arise in mathematical physics in the context of anomalous diffusion and the…
In this work we study constant-coefficient first order systems of partial differential equations and give necessary and sufficient conditions for those systems to have a well posed Cauchy Problem. In many physical applications, due to the…
Two important cases, where boundary conditions and solutions of the well-known integrable equations on a semi-strip are uniquely determined by the initial conditions, are rigorously studied in detail. First, the case of rectangular matrix…
We prove the existence of solutions for some integro-differential systems containing equations with and without the drift terms in the H^2 spaces by virtue of the fixed point technique when the elliptic equations contain second order…
This work is devoted to the study of a nonlocal-in-time evolutional problem for the first order differential equation in Banach space. Our primary approach, although stems from the convenient technique based on the reduction of a nonlocal…
We consider small nonlinear perturbations of linear systems on a time scale with the phase space being finite or infinite-dimensional. For $\Delta$-differential operators, corresponding to linear dynamic systems we consider their…
One standard way to prove existence for deterministic, highly nonlinear PDEs is to use the Schauder-Tychonoff fixed-point theorem. In what follows, we introduce and verify a stochastic variant of the Schauder-Tychonoff theorem. We apply our…
We consider some second order quasilinear partial differential inequalities for real valued functions on the unit ball and find conditions under which there is a lower bound for the supremum of nonnegative solutions that do not vanish at…
This work considers a second order impulsive coupled system of differential equations with generalized jump conditions in half-line, which can depend on the impulses of the unknown functions and their first derivatives. The arguments apply…
In this article we study a class of generalised linear systems of difference equations with given non-consistent initial conditions and infinite many solutions. We take into consideration the case that the coefficients are square constant…
We consider the defocusing nonlinear Schr{\"o}dinger equation in several space dimensions, in the presence of an external potential depending on only one space vari-able. This potential is bounded from below, and may grow arbitrarily fast…
In this article, the existence and uniqueness about the solution for a class of stochastic fractional-order differential equation systems are investigated, where the fractional derivative is described in Caputo sense. The fractional…
We here present a sufficient condition for general arrowing problems to be non definable in first order logic, based in well known tools of finite model theory e.g. Hanf's Theorem and known concepts in finite combinatorics, like senders and…
In this paper we discuss the first order partial differential equations resolved with any derivatives. At first, we transform the first order partial differential equation resolved with respect to a time derivative into a system of linear…
This paper is devoted to studying non-commensurate fractional order planar systems. Our contributions are to derive sufficient conditions for the global attractivity of non-trivial solutions to fractional-order inhomogeneous linear planar…
We prove in this article the well posedness of non - linear Ordinary Differential Equations (ODE) of first and second order in Orlicz spaces with unbounded domain of definition.
The primary focus of this paper is on designing an inexact first-order algorithm for solving constrained nonlinear optimization problems. By controlling the inexactness of the subproblem solution, we can significantly reduce the…
We study necessary conditions and sufficient conditions for the existence of local-in-time solutions of the Cauchy problem for superlinear fractional parabolic equations. Our conditions are sharp and clarify the relationship between the…
Schauder's fixed point theorem is used to derive the existence of solutions to a semilinear heat equation. The equation features a nonlinear term that depends on the time-integral of the unknown on the whole, a priori given, interval of…
We deal with the existence of solutions having L2 regularity for a class of non autonomous evolution equations. Associated with the equation, a general non local condition is studied. The technique we used combines a finite dimensional…