We provide new variational settings to study the a.p. almost periodic solutions of a class of nonlinear neutral delay equations. We extend Shu and Xu 2006 variational setting for periodic solutions of nonlinear neutral delay equation to the almost periodic settings. We obtain results on the structure of the set of the a.p. solutions, results of existence of a.p. solutions, results of existence ...

The paper is concerned with the existence of solution of nonlinear second order neutral stochastic differential inclusions with infinite delay in a Hilbert Space. Sufficient conditions for the existence are obtained by using a fixed point theorem for condensing maps. Keywords—Mild solution, Convex multivalued map, Neutral stochastic differential inclusions.

The paper deals with the oscillation of higher order nonlinear differential equations a neutral term. main results are proved via utilizing an integral criterion as well comparison theorem first-order delay equation whose oscillatory properties known. proposed theorems improve, extend, and simplify existing ones in literature. associated four numerical examples.

Abstract. In this paper, the existence and uniqueness of mild solution is initially obtained by use of measure of noncompactness and simple growth conditions. Then the conditions for approximate controllability are investigated for the distributed second-order neutral stochastic differential system with respect to the approximate controllability of the corresponding linear system in a Hilbert s...