First-order boundary value problem with nonlinear boundary condition on time scales
Summary: This work is concerned with the following first-order dynamic equation on the time scale \(\mathbb T\) \[ x^{\Delta}(t) + p(t)x(\sigma(t)) = f(t, x(t)),\;t \in [0, T]_{\mathbb T} \] with the nonlinear boundary condition \[ x(0) = g(x(\sigma(T))). \] By applying the monotone iterative method, we not only obtain the existence of positive solutions, but also establish iterative schemes for approximating these solutions.
scientific article; zbMATH DE number 5999663
scientific article