in this paper, the stability characteristics of single-walled carbon nanotubes (swcnts) under the action of axial load are investigated. to this end, a nonlocal flügge shell model is developed to accommodate the small length scale effects. the analytical rayleigh-ritz method with beam functions is applied to the variational statement derived from the flügge-type buckling equations. molecular dy...

A finite element method is described for solving Helmholtz type boundary value problems in unbounded regions, including those with infinite boundaries. Typical examples include the propagation of acoustic or electromagnetic waves in waveguides. The radiation condition at infinity is based on separation of variables and differs from the classical Sommerfeld radiation condition. It is shown that ...

In this article, we consider nonlocal p-Laplacian boundary-value problems with integral boundary conditions and a non-negative real-valued boundary condition as a parameter. The main purpose is to study the existence, nonexistence and multiplicity of positive solutions as the boundary parameter varies. Moreover, we prove a sub-super solution theorem, using fixed point index theorems.

In this paper, the existence and uniqueness of a fuzzy solution for the impulsive nonlinear fuzzy integrodifferential equation with nonlocal condition is established via the Banach fixed-point theorem approach and using the fuzzy number whose values are normal, convex, upper semicontinuous, and compactly supported interval.

This paper addresses the influence of boundary conditions and small-scale effect on the free vibration of nano-plates using molecular dynamics (MD) and nonlocal elasticity theory. Based on the MD simulations, Large-scale Atomic/Molecular Massively Parallel Simulator (LAMMPS) is used to obtain fundamental frequencies of single layered graphene sheets (SLGSs) which modeled in this paper as the mo...

In this paper, we consider a semilinear parabolic equation ut = ∆u + u q ∫ t 0 u(x, s)ds, x ∈ Ω, t > 0 with nonlocal nonlinear boundary condition u|∂Ω×(0,+∞) = ∫ Ω φ(x, y)u (y, t)dy and nonnegative initial data, where p, q ≥ 0 and l > 0. The blow-up criteria and the blow-up rate are obtained.

The goal of this paper is to obtain the regularity and the existence of solutions of a retarded semilinear differential equation with nonlocal condition by applying Schauder’s fixed point theorem. We construct the fundamental solution, establish the Hölder continuity results concerning the fundamental solution of its corresponding retarded linear equation, and prove the uniqueness of solutions ...

We investigate nonlocal-interaction energies on the space of probability measures. We establish sharp conditions for the existence of minimizers for a broad class of nonlocalinteraction energies. The condition is closely related to the notion of H-stability of pairwise interaction potentials in statistical mechanics. Our approach uses the direct method of calculus of variations.

|An explicit extrapolated box method is considered for a nonlinear partial integrodif-ferential equation, the Gurtin-MacCamy equation, subject to a nonlocal boundary condition. This problem describes the evolution in time of the age structure of a population. The consistency, stability and convergence properties of the method are studied, and its second order accuracy is demonstrated both analy...

In this paper, we establish a set of sufficient conditions for the controllability of nonlocal impulsive functional integrodifferential evolution systems with finite delay. The controllability results are obtained with out assuming the compactness condition on the evolution operator by using the semigroup theory and applying the fixed point approach. An example is provided to illustrate the the...