Two $C^1$-mappings, whose domain is a connected compact $C^1$-Banach manifold modelled over a Banach space X over $mathbb{K}=mathbb{R}$ or $mathbb{C}$ and whose range is a Banach space Y over $mathbb{K}$, are introduced. Sufficient conditions are given to assert they share only a value. The proof of the result, which is based upon continuation methods, is constructive.