Positive decaying solutions to BVPs with mean curvature operator

A boundary value problem on the whole half-closed interval $[1,\infty)$, associated to differential equations with the Euclidean mean curvature operator or with the Minkowski mean curvature operator is here considered. By using a new approach, based on a linearization device and some properties of principal solutions of certain disconjugate second-order linear equations, the existence of global positive decaying solutions is examined.