×

Multiple positive solutions of a discrete third-order three-point BVP with sign-changing Green’s function. (English) Zbl 1399.39012

Summary: In this paper, by using the Leggett-Williams fixed point theorem, we obtain existence of positive solutions of the following discrete nonlinear third-order three-point boundary value problems: \[ \begin{cases} \Delta ^3u(t - 1) = f(t,u(t)),\, t \in [1,T- 2]_z, \\ \Delta u(0) = u(T) = \Delta ^2(\eta) = 0\end{cases} \] where \(T>4\) is an integer, \(f\in[1,T-2]_z \times[0, \infty)\), \([0, \infty)\) is continuous and
\[ \begin{cases}\eta \in\left[\frac{T-1}{2}, T-2\right]_z T \equiv 1 {\pmod 2}, \\ \eta \in \left[\frac{T-2}{2}, T-2\right]_z T \equiv 0{\pmod 2}.\end{cases} \]

MSC:

39A14 Partial difference equations
39A22 Growth, boundedness, comparison of solutions to difference equations
PDFBibTeX XMLCite