A fixed point theorem for weakly inward A -proper maps and application to a Picard boundary value problem

摘要

A fixed point theorem for weakly inward A-proper maps defined on cones in Banach spaces is established using a fixed point index for such maps. The result generalizes a theorem in Deimling (Nonlinear Functional Analysis, 1985) for weakly inward maps defined on a cone in R n $mathbb{R}^{n}$ . We then apply the theorem to a Picard boundary value problem and obtain the existence of a positive solution.