Some properties of the functional equation ϕ(x)=f(x)+∫0λxg(x,y,ϕ(y))dy
A discussion is given of some of the properties of the functional Volterra Integral equation ϕ(x)=f(x)+∫0λxg(x,y,ϕ(y))dy. and of the corresponding multidimensional equation. Sufficient conditions are given for the uniqueness of the solution, and an iterational process is provided for the constructio...
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| Main Author: | |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
1991-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Subjects: | |
| Online Access: | http://dx.doi.org/10.1155/S0161171291000030 |
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| Summary: | A discussion is given of some of the properties of the functional
Volterra Integral equation
ϕ(x)=f(x)+∫0λxg(x,y,ϕ(y))dy.
and of the corresponding multidimensional equation. Sufficient conditions are
given for the uniqueness of the solution, and an iterational process is provided
for the construction of the solution, together with error estimates. In addition
bounds are provided on the solution. The results obtained are illustrated by
means of the pantograph equation. |
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| ISSN: | 0161-1712 1687-0425 |