this paper proposed analytical solutions for the buckling analysis of rectangular single-layered graphene sheets under in-plane loading on all edges simply is supported. the characteristic equations of the graphene sheets are derived and the analysis formula is based on the nonlocal mindlin plate. this theory is considering both the small length scale effects and transverse shear deformation ef...

Torsional dynamic analysis of carbon nanotubes under the effect of longitudinal magnetic field is carried out in the present study. Torque effect of an axial magnetic field on a carbon nanotube has been defined using Maxwell’s relation. Nonlocal governing equation and boundary conditions for carbon nanotubes are obtained by using Hamilton’s minimum energy principle. Eringen’s nonlocal stress gr...

In this paper an O(h3+l3) L0-stable numerical method is developed for the solution of the heat equation ut = uxx, 0 < x < 1, 0 < t ≤ T , subject to u(x, 0) = f(x), 0 < x < 1, ux(1, t) = g(t), 0 < t < T, and the nonlocal boundary condition R b 0 u(x, t)dx = m(t), 0 < b < 1.

In this paper, we establish the local existence and uniqueness of the solution for the degenerate parabolic equation with a nonlocal source and homogeneous Dirichlet boundary condition. Moreover, we prove that the solution blows up in finite time and obtain the blow-up set in some special case. Mathematics Subject Classification: 35K20, 35K30, 35K65

and Applied Analysis 3 where F x, t ∫ t 0 f x, s ds; one positive solutions for 1.7 was obtained. It is well known that condition AR plays an important role for showing the boundedness of Palais-Smale sequences. More recently, Corrêa and Nascimento in 13 studied a nonlocal elliptic system of p-Kirchhoff type

The correspondance is established between the sigma models , the minimal surfaces and the Monge-Ampére equation. The Lax-Pairs of the minimality condition of the minimal surfaces and the MongeAmpére equations are given. Existance of infinitely many nonlocal conservation laws is shown and some Backlund transformations are also given.

abstract We construct a relativistically covariant symmetry of QED. Previous local and nonlocal symmetries are special cases. This generalized symmetry need not be nilpotent, but nilpotency can be arranged with an auxiliary field and a certain condition. The Noether charge generating the symmetry transformation is obtained, and it imposes a constraint on the physical states.

In this paper we investigate the existence of mild solutions defined on a semiinfinite interval for initial value problems for a differential equation with a nonlocal condition. The results is based on the Schauder-Tychonoff fixed point theorem and rely on a priori bounds on 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.

In this paper, we study a mixed problem with a nonlocal condition for a class of second order singular hyperbolic equations. We prove the existence and uniqueness of a strong solution. The proof is based on a priori estimate and on the density of the range of the operator generated by the studied problem.