This paper is concerned with a 2nth-order p-Laplacian difference equation. By using the critical point method, we establish various sets of sufficient conditions for the nonexistence and existence of solutions for Neumann boundary value problem and give some new results. Results obtained successfully generalize and complement the existing ones.

The variational method and critical point theory are employed to investigate the existence of solutions for 2nth-order difference equation Δ pk−nΔyk−n −1 n f k, yk 0 for k ∈ 1,N with boundary value condition y1−n y2−n · · · y0 0, yN 1 · · · yN n 0 by constructing a functional, which transforms the existence of solutions of the boundary value problem BVP to the existence of critical points for t...

this paper is concerned with a 2nth-order p-laplacian difference equation. by using the critical point method, we establish various sets of sufficient conditions for the nonexistence and existence of solutions for neumann boundary value problem and give some new results. results obtained successfully generalize and complement the existing ones.

For any even positive integer 2n and any positive integermwe construct a class of regular self-adjoint and non-self-adjoint boundary value problems whose spectrum consists of at most (2n − 1)m + 1 eigenvalues. Our main result reduces to previously known results for the cases n = 1 and n = 2. In the self-adjoint case with separated boundary conditions this upper bound can be improved to n(m + 1)...