In this work, we consider a class of nonlinear partial neutral functional di¤erential equations with a nondensely defined Hille-Yosida operator. We first prove the local existence, uniqueness and regularity of solutions. Second, we study the global existence and stability. In the end, we extend in the autonomous case, results of Hale ([21], [23]) concerning dissipativeness and existence of a global attractor to our situation.

We show that ${\rm PD}\sb 4$-complexes with free fundamental group are determined by their intersection pairings and that every hermitian form on a finitely generated free module over the group ring of a free group is realized by some such complex.

The classification of solutions for some dissipative systems by the information of the spectrum is established. Its generator is non self-adjoint Schrödinger operator with rank one singular perturbation. For the proof, a generalized Parseval formula is constructed.

We prove the almost sure invariance principle for a class of abstract dynamical systems including dynamical systems with stretched exponential mixing rates. The result can be applied to chaotic billiards and hyperbolic attractors with Markov sieves as well as expanding maps of the interval and Axiom A diffeomorphisms.

This paper deals with Lindelöf type theorems for monotone Sobolev functions on a uniform domain.