in this paper, we investigate the existence of infinitely many solutions for a bi-nonlocal equation with sign-changing weight functions. we use some natural constraints and the ljusternik-schnirelman critical point theory on c1-manifolds, to prove our main results.

In this paper, we investigate the existence of infinitely many solutions for a bi-nonlocal equation with sign-changing weight functions. We use some natural constraints and the Ljusternik-Schnirelman critical point theory on C1-manifolds, to prove our main results.

The microtubes are important structures in nano electromechanical system .in this study a nonlocal model is presented to investigate the static torsion behavior of microtubes made of bi-directional factionally graded material (BDFGM) subjected to a longitudinal magnetic field. Mechanical properties of BDFGM microtube varies in the radial and longitudinal direction according to an arbitrary func...

A large class of nonlocal equations and nonlocal charges for the Harry Dym hierarchy is exhibited. They are obtained from nonlocal Casimirs associated with its bi-Hamiltonian structure. The Lax representation for some of these equations is also given.

In the present work, the integrable bi-Hamiltonian hierarchies related to compatible nonlocal Poisson brackets of hydrodynamic type are effectively constructed. For achieving this aim, first of all, the problem on the canonical form of a special type for compatible nonlocal Poisson brackets of hydrodynamic type is solved. The compatible pairs of nonlocal Poisson brackets of hydrodynamic type ha...

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...

We introduce the nonlocal Cattaneo-Vernotte equation by including a relaxation effect in the nonlocal diffusion equation, both of which are models for anomalous diffusion. This equation has two different interpretations: as a generalization of Fick’s first law in terms of a nonlocal flux and memory kernel and as an equation arising from the generalized master equation for a continuous time rand...

A mixed initial-boundary value problem for a nonlocal, hyperbolic equation is analyzed with respect to unique solubility and causality. The regularity of the step response and impulse response (the Green functions) is investigated, and a wave front theorem is proved. The problem arises, e.g., at time-varying, electromagnetic, plane wave excitation of stratified, temporally dispersive, bi-isotro...

We model pacemaker effects of an algebraically localized heterogeneity in a 1 dimensional array of oscillators with nonlocal coupling. We assume the oscillators obey simple phase dynamics and that the array is large enough so that it can be approximated by a continuous nonlocal evolution equation. We concentrate on the case of heterogeneities with positive average and show that steady solutions...

We investigate the Cauchy problem for a nonlocal (two-place) FORQ equation. By interpreting this equation as special case of two-component peakon system (exhibiting cubic nonlinearity), we convert into ordinary differential equations in Banach space. Using approach, are able to demonstrate local well-posedness Sobolev space Hs where s>5/2. also establish continuity properties data-to-solution m...