By using the critical point theory, the existence of periodic solutions for 2nth-order nonlinear pLaplacian difference equations is obtained. The main approaches used in our paper are variational techniques and the Saddle Point theorem. The problem is to solve the existence of periodic solutions for 2nth-order p-Laplacian difference equations. The results obtained successfully generalize and co...

By using the critical point theory, the existence of periodic solutions for a 2nth-order nonlinear difference equation containing both advance and retardation involving p-Laplacian is obtained. The main approaches used in our paper are variational techniques and the Saddle Point Theorem. The problem is to solve the existence of periodic solutions for a 2nth-order p-Laplacian difference equation...

We propose a box and ball system with a periodic boundary condition (pBBS). The time evolution rule of the pBBS is represented as a Boolean recurrence formula, an inverse ultradiscretization of which is shown to be equivalent with the algorithm of the calculus for the 2Nth root. The relations to the pBBS of the combinatorial R matrix of U q(A (1) N ) are also discussed.

*Correspondence: [email protected] Department of Mathematics, Inner Mongolia University, Hohhot, 010021, China Abstract The present paper deals with the dependence of eigenvalues of 2nth order boundary value transmission problems on the problem. The eigenvalues depend not only continuously but also smoothly on the problem. Some new differential expressions of eigenvalues with respect to an endpoi...

We state a combinatorial conjecture, which, if true, yields a simple solution to the multiplier version of the inverse problem of the calculus of variations. With the help of a computer, we verified our conjecture for 3 ≤ n ≤ 100, and thus found necessary and sufficient conditions for a 2nth-order scalar ordinary differential equation ∂2nu/∂x2n = f (x, u, ∂u/∂x, . . . , ∂2n−1u/∂x2n−1), 3 ≤ n ≤ ...

The widely-used LMS algorithm for coefficient updates in adaptive (feedforward/decision-feedback) equalizers is found to be suboptimal for ASE-dominant systems but various coefficient-dithering approaches suffer from slow adaptation rate without guarantee of convergence. In view of the non-Gaussian nature of optical noise after the square-law optoelectronic conversion, we propose to apply the h...

We will show how to use the mountain pass theorem to obtain nontrivial solutions of a certain two point BVP for the 2nth order, n ∈ N (formally) self-adjoint nonlinear difference equation n ∑ i=0 [ri(t) u(t − i)] = f (t, u(t)), t ∈ [a, b]Z. No periodicity assumptions will be placed on ri, i = 0, 1, . . . , n or f and it will be assumed that f grows superlinearly both at the origin and at infini...