Abstract. In this survey paper we consider differential and integral equations in locally convex spaces (in particular, in these sequentially complete spaces which contain a compact barrel). We present recently obtained by us results concerning the existence and topological structure of some basic nonlinear equations and we accent applications in our results some theorems of functional analysis.
Keywords. Existence theorems, Kneser type theorems, locally convex spaces containing a compact barrel Sadovski measure of noncompactness.