We study the existence, uniqueness and qualitative properties of global solutions of abstract differential equations with state-dependent delay. Results on the existence of almost periodic-type solutions (including, periodic, almost periodic, asymptotically almost periodic and almost automorphic solutions) are proved. Some examples of partial differential equations with state-dependent delay arising in population dynamics are presented.

We study the existence of solutions for a class of abstract impulsive differential equations. Our technical framework allows us to study partial differential equations with impulsive conditions involving partial derivatives and nonlinear expressions of the solution. Some applications to impulsive partial differential equations are presented.

A model of chemotaxis is analyzed that prevents blow-up of solutions. The modelconsists of a system of nonlinear partial differential equations for the spatial populationdensity of a species and the spatial concentration of a chemoattractant in n-dimensionalspace. We prove the existence of solutions, which exist globally, and are L∞-bounded onfinite time intervals. The hypotheses require nonlocal conditions on the species-inducedproduction of the chemoattractant.