Matches in SemOpenAlex for { <https://semopenalex.org/work/W1574808319> ?p ?o ?g. }
Showing items 1 to 50 of
50
with 100 items per page.
- W1574808319 endingPage "22" @default.
- W1574808319 startingPage "1" @default.
- W1574808319 abstract "In this paper we study integral equations of the form x(t) = a(t) R t 0 C(t,s)x(s)ds with sharply contrasting kernels typ- ified by C � (t,s) = ln(e + (t s)) and D � (t,s) = (1 + (t s)) 1 . The kernel assigns a weight to x(s) and these kernels have exactly opposite effects of weighting. Each type is well represented in the literature. Our first project is to show that for a 2 L 2 (0,1), then solutions are largely indistinguishable regardless of which kernel is used. This is a surprise and it leads us to study the essential dif- ferences. In fact, those differences become large as the magnitude of a(t) increases. The form of the kernel alone projects necessary conditions con- cerning the magnitude of a(t) which could result in bounded so- lutions. Thus, the next project is to determine how close we can come to proving that the necessary conditions are also sufficient. The third project is to show that solutions will be bounded for given conditions on C regardless of whether a is chosen large or small; this is important in real-world problems since we would like to have a(t) as the sum of a bounded, but badly behaved function, and a large well behaved function." @default.
- W1574808319 created "2016-06-24" @default.
- W1574808319 creator A5008162110 @default.
- W1574808319 date "2008-01-01" @default.
- W1574808319 modified "2023-09-24" @default.
- W1574808319 title "Integral equations with contrasting kernels" @default.
- W1574808319 cites W1989439280 @default.
- W1574808319 cites W2000805868 @default.
- W1574808319 cites W2012749358 @default.
- W1574808319 cites W2029762292 @default.
- W1574808319 cites W2042971422 @default.
- W1574808319 cites W2074412622 @default.
- W1574808319 cites W3047978349 @default.
- W1574808319 doi "https://doi.org/10.14232/ejqtde.2008.1.2" @default.
- W1574808319 hasPublicationYear "2008" @default.
- W1574808319 type Work @default.
- W1574808319 sameAs 1574808319 @default.
- W1574808319 citedByCount "1" @default.
- W1574808319 countsByYear W15748083192020 @default.
- W1574808319 crossrefType "journal-article" @default.
- W1574808319 hasAuthorship W1574808319A5008162110 @default.
- W1574808319 hasBestOaLocation W15748083191 @default.
- W1574808319 hasConcept C134306372 @default.
- W1574808319 hasConcept C28826006 @default.
- W1574808319 hasConcept C33923547 @default.
- W1574808319 hasConceptScore W1574808319C134306372 @default.
- W1574808319 hasConceptScore W1574808319C28826006 @default.
- W1574808319 hasConceptScore W1574808319C33923547 @default.
- W1574808319 hasIssue "2" @default.
- W1574808319 hasLocation W15748083191 @default.
- W1574808319 hasLocation W15748083192 @default.
- W1574808319 hasLocation W15748083193 @default.
- W1574808319 hasOpenAccess W1574808319 @default.
- W1574808319 hasPrimaryLocation W15748083191 @default.
- W1574808319 hasRelatedWork W2050770628 @default.
- W1574808319 hasRelatedWork W2052109794 @default.
- W1574808319 hasRelatedWork W2141704600 @default.
- W1574808319 hasRelatedWork W2401850100 @default.
- W1574808319 hasRelatedWork W2910133962 @default.
- W1574808319 hasRelatedWork W3117324600 @default.
- W1574808319 hasRelatedWork W3161443230 @default.
- W1574808319 hasRelatedWork W4210327724 @default.
- W1574808319 hasRelatedWork W4226067901 @default.
- W1574808319 hasRelatedWork W4313705710 @default.
- W1574808319 isParatext "false" @default.
- W1574808319 isRetracted "false" @default.
- W1574808319 magId "1574808319" @default.
- W1574808319 workType "article" @default.