Three-point boundary value problems for second-order discrete equations
The authors present existence results for solutions to the following discrete equations: \[ \begin{aligned} D^2y_{k+1} & =f(x_k,y_k,Dy_k),\quad k=1,\dots,n-1,\\ (0,0) & = G(y_0,y_n,y_d),\quad d\in\{1,\dots,n-1\},\end{aligned} \] which approximate the three-point boundary value problem: \[ \begin{aligned} y'' & =f(x,y,y'),\quad 0\leq x\leq 1,\\ (0,0)& =G(y(0),y(1),y(a)),\quad 0<a<1,\end{aligned} \] where \(f\) and \(G\) are continuous and perhaps nonlinear functions.
second-order ordinary differential equations
scientific article; zbMATH DE number 2082244
scientific article