Three-point boundary value problems for difference equations. (English) Zbl 1075.39015

The authors consider the discrete nonlinear difference equation \(\Delta^2x_{k-1} +f(x_k)=0\) together with a three point boundary condition \(x_0=0\), \(x_{n+1} = ax_\ell+b\). By means of Krasnoselskii’s fixed point theorem they prove results on (non-)existence and uniqueness of positive solutions. Finally they point out an application to a discrete model of heat conduction.


39A12 Discrete version of topics in analysis
34B15 Nonlinear boundary value problems for ordinary differential equations
39A11 Stability of difference equations (MSC2000)
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