An existence of an isolated solution to nonlinear two-point boundary value problem with parameter
The authors use the parametrization method to study the nonlinear two-point boundary value problem \[ x' = f(t, x, \mu), t \in (0, T), x \in \mathbb{R}^n, \mu \in \mathbb{R}^m, g(\mu, x(0), x(T)) = 0, \] where \(f: [0, T]\times \mathbb{R}^n \times \mathbb{R}^m\to \mathbb{R}^n\), \(g: \mathbb{R}^m \times \mathbb{R}^n \times \mathbb{R}^n \to \mathbb{R}^{n+m}\) are continuous. The method consists in partition of the interval apart, the introduction of additional parameters and reducing the original problem to the equivalent multi-point boundary value problem with parameters. The algorithms for finding a solution to an equivalent boundary value problem are constructed. The conditions for convergence of the algorithms that ensure the solvability of nonlinear two-point boundary value problem with parameter are obtained.
nonlinear two-point boundary value problem with parameter
scientific article; zbMATH DE number 7350136
scientific article