Boundary value problems for second-order nonlinear difference equations with discrete φ-Laplacian and singular φ

In this article, we study the existence and multiplicity of solutions for boundary value problems of the type del[phi(Delta x(k))] + f(k)(x(k), Delta x(k)) = 0 (2 <= k <= n-1), l(x, Delta x) = 0, where phi : (-a, a) -> R denotes an increasing homeomorphism such that phi(0) = 0 and 0 < a < infinity, l(x, Delta x) = 0 denotes the Dirichlet, periodic or Neumann boundary conditions and f(k) (2 <= k <= n - 1) are continuous functions. Our main tool is Brouwer degree together with fixed point reformulations of the above problems.