Existence and properties of Schlicht integral manifolds

In this paper the existence and properties of integral manifolds passing through initial surfaces are investigated. A new approach via non-local assumptions, cone-valued metrics and comparison problems allows to weaken the conditions guaranteeing that the manifolds are graphs of smooth functions. By means of comparison theorems for fixed-point problems the attractivity and the existence of asymptotic phases are investigated and the estimates are improved. Supported by Alexander von Humboldt-Stiftung.