Absence of eigenvalues for integro-differential operators with periodic coefficients.
Backward Euler type methods for parabolic integro-differential equations in Banach space
Boundary value problems for elliptic integro-differential operators.
Bourgin–Yang-type theorem for -compact perturbations of closed operators. I: The case of index theories with dimension property.
Characteristic equations for the spectrum of generators
Coercivité de formes sesquilinéaires intégro-différentielles dans des espaces de Sobolev avec poids
Existence of solutions for some Hammerstein type integro-differential inclusions.
Fractional integrodifferentiation in Hölder classes of arbitrary order.
Global existence for a semilinear prabolic Volterra equation.
Heat kernel estimates for critical fractional diffusion operators
We construct the heat kernel of the 1/2-order Laplacian perturbed by a first-order gradient term in Hölder spaces and a zero-order potential term in a generalized Kato class, and obtain sharp two-sided estimates as well as a gradient estimate of the heat kernel, where the proof of the lower bound is based on a probabilistic approach.
Heat kernel estimates for the Dirichlet fractional Laplacian
We consider the fractional Laplacian on an open subset in with zero exterior condition. We establish sharp two-sided estimates for the heat kernel of such a Dirichlet fractional Laplacian in open sets. This heat kernel is also the transition density of a rotationally symmetric -stable process killed upon leaving a open set. Our results are the first sharp twosided estimates for the Dirichlet heat kernel of a non-local operator on open sets.
Hölder continuity of solutions of second-order non-linear elliptic integro-differential equations
This paper is concerned with the Hölder regularity of viscosity solutions of second-order, fully non-linear elliptic integro-differential equations. Our results rely on two key ingredients: first we assume that, at each point of the domain, either the equation is strictly elliptic in the classical fully non-linear sense, or (and this is the most original part of our work) the equation is strictly elliptic in a non-local non-linear sense we make precise. Next we impose some regularity and growth...
Integro-differential equations with time-varying delay
Integro-differential equations with time-varying delay can provide us with realistic models of many real world phenomena. Delayed Lotka-Volterra predator-prey systems arise in ecology. We investigate the numerical solution of a system of two integro-differential equations with time-varying delay and the given initial function. We will present an approach based on -step methods using quadrature formulas.
Maximum principles, sliding techniques and applications to nonlocal equations.
Nonlinear mixed Volterra-Fredholm integrodifferential equation with nonlocal condition
The aim of the present paper is to investigate the global existence of mild solutions of nonlinear mixed Volterra-Fredholm integrodifferential equations, with nonlocal condition. Our analysis is based on an application of the Leray-Schauder alternative and rely on a priori bounds of solutions.
On a class of abstract degenerate fractional differential equations of parabolic type
In this paper, we investigate a class of abstract degenerate fractional differential equations with Caputo derivatives. We consider subordinated fractional resolvent families generated by multivalued linear operators, which do have removable singularities at the origin. Semi-linear degenerate fractional Cauchy problems are also considered in this context.
On a class of diffeomorphisms defined by integro-differential operators
We study an integro-differential operator Φ: H̅¹ → L² of Fredholm type and give sufficient conditions for Φ to be a diffeomorphism. An application to functional equations is presented.
On a class of parabolic integro-differential equations.
On a Singular Value Problem for the Fractional Laplacian on the Exterior of the Unit Ball
2000 Mathematics Subject Classification: Primary 26A33; Secondary 47G20, 31B05We study a singular value problem and the boundary Harnack principle for the fractional Laplacian on the exterior of the unit ball.
On one class of operators associated with differential equations of fractional order.