This article is dedicated to the proof of the existence of classical solutions for a class of non-linear integral variational problems. Those problems are involved in nonlocal image and signal processing.

We present some new formulae for the solution of boundary value problems for a two-dimensional isotropic elastic body. In particular, using the so-called Dbar formalism and the method introduced by Fokas (2008) [4], we obtain integral representations of the Fourier type for the displacements appearing in boundary value problems formulated in an arbitrary convex polygon with n sides. © 2011 Else...

We exploit a recently developed nonlocal vector calculus to provide a variational analysis for a general class of nonlocal diffusion problems given by a linear integral equation on bounded domains in R. The ubiquity of the nonlocal operator is illustrated by a number of applications ranging from continuum mechanics to graph theory. These applications elucidate different interpretations of the o...

Nonlinear Analysis B: in press, 2004. The Swift-Hohenberg fluid convection system with both local and nonlocal nonlinearities under the influence of white noise is studied. The objective is to understand the difference in the dynamical behavior in both local and nonlocal cases. It is proved that when sufficiently many of its Fourier modes are forced, the system has a unique invariant measure, o...

The following article investigates buckling of moderately thick circular Nano plates with an orthotropic property under uniform radial compressive in-plane mechanical load. Taking into account nonlocal elasticity theory (Eringen), principle of virtual work, first order shear deformation plate theory (FSDT) and nonlinear Von-Karman strains, the governing equations are obtained based on displacem...

This study presents a fractional-order continuum mechanics approach that allows combining selected characteristics of nonlocal elasticity, typical classical integral and gradient formulations, under single frame-invariant framework. The resulting generalized theory is capable capturing both stiffening softening effects it not subject to the inconsistencies often observed external loads boundary...

In this paper using a fixed point theory on a cone we present some new results on the existence of multiple positive solutions for singular nonlocal boundary value problems involving integral conditions with derivative dependence.

In this paper, we study a parabolic equation with purely nonlocal (integral) conditions. We present a numerical approximate solution by Laplace transform method. Some experimental numerical results using the proposed numerical procedure are discussed.

We study existence and stability of homoclinic type solutions of a bistable integral equation. These are stationary solutions of an integrodifferential equation, which is a gradient flow for a free energy functional with general nonlocal integrals penalizing spatial nonuniformity.