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 |
| Summary: | 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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| ISSN: | 0161-1712 1687-0425 |