Approximate solution of nonlinear multi-point boundary value problem on the half-line (Q2884914)

The authors investigate the following nonlinear problem with multi-point boundary conditions NEWLINE\[NEWLINE \begin{aligned} & x''(t) - p x'(t) - q x(t) = f(t, x(t)),\quad t\in[0, +\infty), \\ & \alpha x(0) - \beta x'(0) - \sum_{i=1}^{n} k_{i} x(\xi_{i}) = a_{0},\quad \lim_{t\to +\infty} \frac{x(t)}{\operatorname{e}^{r t}} = b_{0}, \end{aligned} NEWLINE\]NEWLINE where \(p\), \(q\), \(\xi_{i}\), \(a\), \(b\) are nonnegative real numbers, \(r\in(0, \frac{p+\sqrt{p^{2}+4q}}{2}]\), \(f\) is a continuous function and \(\alpha\), \(\beta\), \(k_{i}\geq 0\) satisfy \(\alpha^{2} + \beta^{2} \neq 0\). The authors provide an efficient algorithm to solve the nonlinear problem on the half-line. Their approach is based on the orthogonal basis established in the reproducing kernel space. Moreover, the uniform convergence of the approximate solution is investigated.