Asymptotics of the fundamental system of solutions of a linear functional-differential equation with respect to a parameter
We study a functional-differential equation, where F is a linear operator acting from the Hölder space Hγ into the Sobolev space W p s [0, 1] and ρ is a complex parameter. For large absolute values of ρ, we construct a one-to-one correspondence between the solutions x(ρ;t) and y(ρ;t) of the equation...
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| Date: | 1995 |
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| Main Authors: | , |
| Format: | Article |
| Language: | Russian English |
| Published: |
Institute of Mathematics, NAS of Ukraine
1995
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| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/5475 |
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| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
| Download file: |  |
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Ukrains’kyi Matematychnyi Zhurnal| Summary: | We study a functional-differential equation, where F is a linear operator acting from the Hölder space Hγ into the Sobolev space W p s [0, 1] and ρ is a complex parameter. For large absolute values of ρ, we construct a one-to-one correspondence between the solutions x(ρ;t) and y(ρ;t) of the equations
and y(n)+ρyn=0. We also establish conditions that should be imposed on the operatorF in order that specially selected fundamental systems of solutions of these equationsx j (ρ;t) andy j (ρ;t), j=1,...,n, satisfy the estimate
with constantsc, κ>0 for the functional space. |
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