Das Rand-Anfangswertproblem für quasilineare Wellengleichungen in Sobolevräumen niedriger Ordnung.
We consider an initial boundary value problem for the equation . We first prove local and global existence results under suitable conditions on f and g. Then we show that weak solutions decay either algebraically or exponentially depending on the rate of growth of g. This result improves and includes earlier decay results established by the authors.
The Leray-Schauder degree is extended to certain multi-valued mappings on separable Hilbert spaces with applications to the existence of weak periodic solutions of discontinuous semilinear wave equations with fixed ends.