Nonlinear Volterra delay evolution inclusions subjected to nonlocal initial conditions

This paper deals with a nonlinear Volterra delay evolution inclusion subjected to a nonlocal implicit initial condition. The evolution inclusion involves an $m$-dissipative operator (possibly multivalued and/or nonlinear) and a noncompact interval. We first consider the evolution inclusion subjected to a local initial condition and prove an existence result for bounded $C^0$-solutions. Then, using a fixed point theorem for upper semicontinuous multifunctions with contractible values, we obtain a global solvability result for the original problem. Finally, we present an example to illustrate the abstract result.

Almost semicontinuous multifunctions via ideals

The aim of this paper is to introduce and study upper and lower almost semi-I-continuous multifunctions as a generalization of upper and lower semi-I-continuous multifunctions, respectively.

Some nonoscillation criteria for inclusions

New nonoscillatory criteria are presented for second order differential inclusions. The theory relies on Ky Fan's fixed point theorem for upper semicontinuous multifunctions.