An integral equation associated with linear homogeneous differential equations
Associated with each linear homogeneous differential equation y(n)=∑i=0n−1ai(x)y(i) of order n on the real line, there is an equivalent integral equation f(x)=f(x0)+∫x0xh(u)du+∫x0x[∫x0uGn−1(u,v)a0(v)f(v)dv]du which is satisfied by each solution f(x) of the differential equation.
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| Format: | Article |
| Language: | English |
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Hindawi Limited
1986-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
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| Online Access: | http://dx.doi.org/10.1155/S0161171286000509 |
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Article |
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doaj-9871dc70491146eabe83204ae8e23c162020-11-24T23:31:05ZengHindawi LimitedInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251986-01-019240540810.1155/S0161171286000509An integral equation associated with linear homogeneous differential equationsA. K. Bose0Department of Mathematical Sciences, Clemson University, Clemson 29631, South Carolina, USAAssociated with each linear homogeneous differential equation y(n)=∑i=0n−1ai(x)y(i) of order n on the real line, there is an equivalent integral equation f(x)=f(x0)+∫x0xh(u)du+∫x0x[∫x0uGn−1(u,v)a0(v)f(v)dv]du which is satisfied by each solution f(x) of the differential equation.http://dx.doi.org/10.1155/S0161171286000509linear homogeneous differential equationsintegral equationsinitial value problemsvariation of parameters formulauniform convergence. |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
A. K. Bose |
| spellingShingle |
A. K. Bose An integral equation associated with linear homogeneous differential equations International Journal of Mathematics and Mathematical Sciences linear homogeneous differential equations integral equations initial value problems variation of parameters formula uniform convergence. |
| author_facet |
A. K. Bose |
| author_sort |
A. K. Bose |
| title |
An integral equation associated with linear homogeneous differential equations |
| title_short |
An integral equation associated with linear homogeneous differential equations |
| title_full |
An integral equation associated with linear homogeneous differential equations |
| title_fullStr |
An integral equation associated with linear homogeneous differential equations |
| title_full_unstemmed |
An integral equation associated with linear homogeneous differential equations |
| title_sort |
integral equation associated with linear homogeneous differential equations |
| publisher |
Hindawi Limited |
| series |
International Journal of Mathematics and Mathematical Sciences |
| issn |
0161-1712 1687-0425 |
| publishDate |
1986-01-01 |
| description |
Associated with each linear homogeneous differential equation y(n)=∑i=0n−1ai(x)y(i) of order n on the real line, there is an equivalent integral equation f(x)=f(x0)+∫x0xh(u)du+∫x0x[∫x0uGn−1(u,v)a0(v)f(v)dv]du which is satisfied by each solution f(x) of the differential equation. |
| topic |
linear homogeneous differential equations integral equations initial value problems variation of parameters formula uniform convergence. |
| url |
http://dx.doi.org/10.1155/S0161171286000509 |
| work_keys_str_mv |
AT akbose anintegralequationassociatedwithlinearhomogeneousdifferentialequations AT akbose integralequationassociatedwithlinearhomogeneousdifferentialequations |
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