Positive solutions to a nonlinear Abel-type integral equation on the whole line (Q5948756)
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: Positive solutions to a nonlinear Abel-type integral equation on the whole line |
scientific article; zbMATH DE number 1671980
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Positive solutions to a nonlinear Abel-type integral equation on the whole line |
scientific article; zbMATH DE number 1671980 |
Statements
Positive solutions to a nonlinear Abel-type integral equation on the whole line (English)
0 references
12 November 2001
0 references
nonlinear Volterra integral equations
0 references
blow-up solutions
0 references
positive solutions
0 references
0.91741997
0 references
0.91077197
0 references
0.9075022
0 references
0 references
0.90421635
0 references
0.9036969
0 references
The authors consider the following nonlinear Volterra-type integral equation on the whole real line: NEWLINE\[NEWLINEu(x)=\int_{-\infty}^x (x - s)^{\alpha-1} g(u(s)) \quad(\alpha\geq 1) NEWLINE\]NEWLINE where g is a continuous, nondecreasing function such that \(g(0) = 0\). It is shown that the equation always has nontrivial solutions. Moreover, necessary and sufficient conditions for the existence of positive solutions are established. A condition is also provided which ensures that all the nontrivial solutions have the blow-up property.
0 references
