We establish some new criteria for the oscillation of third-order difference equations of the form Delta((1/a(2)(n))(Delta(1/a(1)(n))(Delta x(n))(alpha 1))(alpha 2)) + delta q(n)f(x[g(n)]) = 0, where Delta is the forward ...

In this paper we shall employ the nonlinear alternative of Leray-Schauder and known sign properties of a related Green's function to establish the existence results for the nth-order discrete focal boundary-value problem. ...

In this paper we establish the existence of two nonnegative solutions to singular (n, p) and singular (p, n - p) focal boundary value problems. Our nonlinearity f(t, y) may be singular at y = 0, t = 0 and/or t = 1.

A general existence theory is presented for initial value problems where our nonlinearity may be singular in its dependent variable and may also change sign.