Related papers: A unified existence theory for evolution equations…
In this paper, we study stability properties of nonuniform hyperbolicity for evolution processes associated with differential equations in Banach spaces. We prove a robustness result of nonuniform hyperbolicity for linear evolution…
In this paper we analyze a broad class of abstract doubly nonlinear evolution equations in Banach spaces, driven by nonsmooth and nonconvex energies. We provide some general sufficient conditions, on the dissipation potential and the energy…
We consider evolution differential equations in Fr\'echet spaces that possess unconditional Schauder basis and construct a version of the majorant functions method to obtain existence theorems for Cauchy problems. Applications to PDE and…
We offer in this short report a simple Monte-Carlo method for solving a well-posed non-linear integral equations of second Fredholm's and Volterra's type and built a confidence region for solution in an uniform norm, applying the grounded…
In this note we develop a framework which allows to prove an abstract existence result for non-linear evolution equations involving so-called non-induced operators, i.e., operators which are not prescribed by a time-dependent family of…
In this note we develop a framework which allows to prove an existence result for non-linear evolution problems involving time-dependent, pseudo-monotone operators. This abstract existence result is applicable to a large class of concrete…
We prove that a first order linear differential operator G with unbounded operator coefficients is Fredholm on spaces of functions on the real line with values in a reflexive Banach space if and only if the corresponding strongly continuous…
The Fredholm index of unbounded operators defined on generalized solutions of nonlocal elliptic problems in plane bounded domains is investigated. It is known that nonlocal terms with smooth coefficients having zero of a certain order at…
This paper ascertains the global behavior of the forward and backward branches of solutions provided by the Leray-Schauder continuation theorem for orientable $\mathcal{C}^1$ Fredholm maps, as developed by the authors in [54]. Under…
We study neural field equations, which are prototypical models of large-scale cortical activity, subject to random data. We view this spatially-extended, nonlocal evolution equation as a Cauchy problem on abstract Banach spaces, with…
In this paper we study well posedness of a certain nonlinear Volterra-Fredholm dynamic integral and integro-dynamic equations on unbounded interval from arbitrary time scale. We derive the time scale analogue of certain integral…
In this article we discuss the solvability of some class of fully nonlinear equations, and equations with p-Laplacian in more general conditions by using a new approach given in [1] for studying the nonlinear continuous operator. Moreover…
For nonuniform exponentially bounded evolution families defined on Banach spaces, we introduce a class of Banach function spaces, whose norms are completely determined by the nonuniform behaviour of the corresponding evolution family. We…
We show that a certain class of nonlocal scalar models, with a kinetic operator inspired by string field theory, is equivalent to a system which is local in the coordinates but nonlocal in an auxiliary evolution variable. This system admits…
We prove necessary conditions for Fredholmness of singular integral operators with piecewise continuous coefficients on weighted Banach function spaces. These conditions are formulated in terms of indices of submultiplicative functions…
In this paper, we establish some new variants of fixed point theorems for a large class of countably nonexpansive multi-valued mappings. Some fixed point theorems for the sum and the product of three multi-valued mappings defined on…
Problem for the first order differential equation with an unbounded operator coefficient in Banach space and nonlinear nonlocal condition is considered. A numerical method is proposed and justified for the solution of this problem under…
We adapt the classical theory of local well-posedness of evolution problems to cases in which the nonlinearity can be accurately quantified by two different norms. For ordinary differential equations, we consider $\dot{x} = f(x,x)$ for a…
By means of two fractional order integral inequalities we investigate the existence and uniqueness of the solutions of the fractional nonlinear Volterra integral equation and a fractional nonlinear integrodifferential equation in Banach…
Combining monotonicity theory related to the parametric version of the Browder-Minty Theorem with fixed point arguments we obtain hybrid existence results for a system of two operator equations. Applications are given to a system of…