Orders of solutions of an n-th order linear differential equation with entire coefficients
We study the solutions of the differential equation $$ f^{(n)}+A_{n-1}(z) f^{(n-1) }+dots+A_{1}(z)f'+A_{0}(z) f=0, $$ where the coefficients are entire functions. We find conditions on the coefficients so that every solution that is not identically zero has infinite order.
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Texas State University
2001-09-01
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| Series: | Electronic Journal of Differential Equations |
| Subjects: | |
| Online Access: | http://ejde.math.txstate.edu/Volumes/2001/61/abstr.html |
| Summary: | We study the solutions of the differential equation $$ f^{(n)}+A_{n-1}(z) f^{(n-1) }+dots+A_{1}(z)f'+A_{0}(z) f=0, $$ where the coefficients are entire functions. We find conditions on the coefficients so that every solution that is not identically zero has infinite order. |
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| ISSN: | 1072-6691 |