In [8] the notion of “projected differential equation” has been introduced and the stability of solutions has been studied by means of Stampacchia type variational inequalities. More recently, in [20], Minty variational inequalities have been involved in the study of properties of the trajectories of such a projected differential equation. We consider classical generalizations of both problems,...

Abstract It has become imperative in recent times to determine the properties of the solutions of certain mathematical equations or inequalities from the knowledge of associated inequalities or equations. In this paper, a number of oscillatory properties of the solutions of impulsive differential inequalities are established using the knowledge of those of their associated equations and what is...

We develop the theory of twisted L-cohomology and twisted spectral invariants for flat Hilbertian bundles over compact manifolds. They can be viewed as functions on H(M, R) and they generalize the standard notions. A new feature of the twisted L-cohomology theory is that in addition to satisfying the standard L Morse inequalities, they also satisfy certain asymptotic L Morse inequalities. These...