ABSTRACT
Let X be a Banach space consisting of certain uniformly continuous functions on a metric space W. For T a Lipschitz function from X to X, it can be shown in some cases that Tf satisfies a Lipschitz condition if f does, for f in X. This leads to invariant set criteria, that is, criteria are found in order that T(J) Ì J holds for certain subsets J of X. This is applied to give criteria for the existence of invariant sets for certain quasicontractive semigroups of operators on X. Examples include the Hamilton-Jacobi equation and a nonlinear parabolic equation.
