Electron. J. Differential Equations, Vol. 2023 (2023), No. 63, pp. 1-55.

Abstract degenerate Volterra inclusions in locally convex spaces

Marko Kostić

In this article, we analyze the abstract degenerate Volterra integro-differential equations in sequentially complete locally convex spaces by using multivalued linear operators and vector-valued Laplace transform. We follow the method which is based on the use of (a,k)-regularized \(C\)-resolvent families generated by multivalued linear operators and which suggests a very general way of approaching abstract Volterra equations. Among many other themes, we consider the Hille-Yosida type theorems for (a,k)-regularized C-resolvent families, differential and analytical properties of (a,k)-regularized C-resolvent families, the generalized variation of parameters formula, and subordination principles. We also introduce and analyze the class of (a,k)-regularized (C_1,C_2)-existence and uniqueness families. The main purpose of third section, which can be viewed of some independent interest, is to introduce a relatively simple and new theoretical concept useful in the analysis of operational properties of Laplace transform of non-continuous functions with values in sequentially complete locally convex spaces. This concept coincides with the classical concept of vector-valued Laplace transform in the case that X is a Banach space.

Submitted July 10, 2022. Published September 25, 2023.
Math Subject Classifications: 34G25, 45D05, 47D06, 46G12, 47D60, 47D62.
Key Words: Abstract degenerate Volterra inclusion; locally convex space; Abstract degenerate fractional differential equation; (a,k)-regularized C-resolvent family; multivalued linear operator.
DOI: 10.58997/ejde.2023.63

Show me the PDF file (631 KB), TEX file for this article.

Marko Kostić
University of Novi Sad
Faculty of Technical Sciences
Trg D. Obradovića 6
21125 Novi Sad, Serbia
email: markokostic121@yahoo.com

Return to the EJDE web page