Topological and geometrical methods in nonlinear higher order elliptic equations and related (second order) parabolic problems

The main focus of the present project is on higher (i.e. at least 4th) order elliptic problems. Here, many of those methods familiar from second order equations do not work at all or need at least a fundamental modification. In order to gain a better understandingof nonlinear higher order equations in general we try to find out to which extent results from second order equations can be extended and generalized to higher order equations. The needed techniques are more involved and in many situations completely different.Beside our investigations on higher order elliptic equations we want to study the dynamical behaviour in certain semilinear parabolic equations, which are closely related to the stationary problems discussed in the first part.With these investigations we hope to form a basis for further investigations in higher order {\it parabolic} problems too. These are even more involved than higher order elliptic problems since they are known to enjoy no positivity preserving property at all.