Three positive solutions to a discrete focal boundary value problem (Q1381716)

On the basis of two known fixed point theorems in real Banach space with a cone, the authors prove three theorems concerning the existence of at least three positive solutions to the focal boundary value problem \[ \Delta^3 x(t-k) +f\bigl(x(t) \bigr)=0, \quad \text{for all } t\in[a+k, b+k],\;k\in \{1,2\}, \] \[ \Delta x(a)= \Delta x(t_2) =\Delta^2 x(b+1) =0, \] where \(f:\mathbb{R} \to\mathbb{R}\) is continuous and \(f(x)\geq 0\) if \(x\geq 0\).