Using the three critical points theorem by B. Ricceri [23], we obtain a multiplicity result for a class of nonlocal problems in OrliczSobolev spaces. To our knowledge, this is the first contribution to the study of nonlocal problems in this class of functional spaces.

We construct the covariant nonlocal action for recently suggested long-distance modifications of gravity theory motivated by the cosmological constant and cos-mological acceleration problems. This construction is based on the special non-local form of the Einstein-Hilbert action explicitly revealing the fact that this action within the covariant curvature expansion begins with curvature-squared...

We construct the covariant nonlocal action for recently suggested long-distance modifications of gravity theory motivated by the cosmological constant and cos-mological acceleration problems. This construction is based on the special non-local form of the Einstein-Hilbert action explicitly revealing the fact that this action within the covariant curvature expansion begins with curvature-squared...

Nonlocal problems is a major research area in many branches of modern physics, biotechnology, chemistry and engineering, which arises when it is impossible to determine the boundary values of unknown function and its derivatives. Increasingly often, there arise problems with nonlocal integral boundary conditions, especially in particle diffusion [1] and heat conduction [2, 3]. Partial different...

We study Neumann type boundary value problems for nonlocal equations related to Lévy processes. Since these equations are nonlocal, Neumann type problems can be obtained in many ways, depending on the kind of “reflection” we impose on the outside jumps. To focus on the new phenomenas and ideas, we consider different models of reflection and rather general non-symmetric Lévy measures, but only s...

Nonlocal problems for hyperbolic equations of the first order describe the dynamic of population [1]–[3]. During the last thirty years the existence and uniqueness of the solution of nonlocal problems for the system of hyperbolic equations have been considered in a number of papers [4]–[8]. The authors assumed that the nonlinear functions satisfy the Lipschitz condition with respect to the unkn...

We establish sharp boundary regularity estimates in C and C domains for nonlocal problems of the form Lu = f in Ω, u = 0 in Ω. Here, L is a nonlocal elliptic operator of order 2s, with s ∈ (0, 1). First, in C domains we show that all solutions u are C up to the boundary and that u/d ∈ C(Ω), where d is the distance to ∂Ω. In C domains, solutions are in general not comparable to d, and we prove a...

Keywords: Elliptic equations Nonlocal boundary value problems Difference schemes Stability a b s t r a c t The well-posedness of the Bitsadze–Samarskii type nonlocal boundary value problem in Hölder spaces with a weight is established. The coercivity inequalities for the solution of the nonlocal boundary value problem for elliptic equations are obtained. The stable second order of accuracy diff...

We present a model for nonlocal diffusion with Neumann boundary conditions in a bounded smooth domain prescribing the flux through the boundary. We study the limit of this family of nonlocal diffusion operators when a rescaling parameter related to the kernel of the nonlocal operator goes to zero. We prove that the solutions of this family of problems converge to a solution of the heat equation...

In this paper, a scalar peridynamic model is analyzed. The study extends earlier works in the literature on nonlocal diffusion and nonlocal peridynamic models to include a sign changing kernel. We prove the well-posedness of both variational problems with volume constraints and time-dependent equations with or without damping. The analysis is based on some nonlocal Poincaré type inequalities an...