The set of solutions for abstract Volterra equations in \(L^p([0,a],\mathbb{R}^m)\) (Q1975298)
From MaRDI portal
 | This is the item page for this Wikibase entity, intended for internal use and editing purposes. Please use this page instead for the normal view: The set of solutions for abstract Volterra equations in \(L^p([0,a],\mathbb{R}^m)\) |
scientific article; zbMATH DE number 1428521
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | The set of solutions for abstract Volterra equations in \(L^p([0,a],\mathbb{R}^m)\) |
scientific article; zbMATH DE number 1428521 |
Statements
The set of solutions for abstract Volterra equations in \(L^p([0,a],\mathbb{R}^m)\) (English)
0 references
9 April 2000
0 references
Let \(F\) be an abstract Volterra operator on a Banach space \(E\). In the literature there are a few results on the topological structure of the solution set of the equation \(x=F(x)\) in the case of some Banach spaces. In the paper under review a similar result is proved in the space \(E=L^p ([0,a], \mathbb{R}^n)\). An application of the obtained result to the Hammerstein integral equation is presented.
0 references
abstract Volterra equations
0 references
Banach space
0 references
topological structure of the solution set
0 references
Hammerstein integral equation
0 references
