1. Degenerate abstract Volterra equations in locally convex spaces
- Author
-
Marko Kostić
- Subjects
Discrete mathematics ,Pure mathematics ,General Mathematics ,010102 general mathematics ,Scalar (mathematics) ,Degenerate energy levels ,Volterra equations ,Equicontinuity ,01 natural sciences ,Volterra integral equation ,010101 applied mathematics ,symbols.namesake ,Locally convex topological vector space ,Resolvent operator ,symbols ,0101 mathematics ,Well posedness ,Mathematics - Abstract
In the paper under review, we analyze various types of degenerate abstract Volterra integrodifferential equations in sequentially complete locally convex spaces. From the theory of non-degenerate equations, it is well known that the class of (a,k)-regularized C-resolvent families provides an efficient tool for dealing with abstract Volterra integro-differential equations of scalar type. Following the approach of T.-J. Xiao and J. Liang [41]-[43], we introduce the class of degenerate exponentially equicontinuous (a,k)- regularized C-resolvent families and discuss its basic structural properties. In the final section of paper, we will look at generation of degenerate fractional resolvent operator families associated with abstract differential operators.
- Published
- 2017