2010; Physical and Mathematical Sciences, 44(1 (221): 22–26
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NEUMANN PROBLEM FOR FOURTH ORDER DEGENERATE ORDINARY DIFFERENTIAL EQUATIONS

L. P. Tepoyan*

Received: 2025-02-27 · Published: 2010-01-26

© 2010 The Author(s) and the original publisher.

CC BY 4.0 This work is licensed under a Creative Commons Attribution 4.0 International License.
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Original title
NEUMANN PROBLEM FOR FOURTH ORDER DEGENERATE ORDINARY DIFFERENTIAL EQUATIONS
Author
L. P. Tepoyan
Published
2010-01-26
Licence
Creative Commons Attribution 4.0 International

Abstract

In the present paper the Neumann problem for the equation Lu≡(tαuα)″+au+f, where 0≤α≤4, t∈[0,b], f∈L2(0,b) , is considered. Firstly, the weighted Sobolev space Wα2 and generalized solution for the abovementioned equation are defined. Then, the existence and uniqueness of the generalized solution is studied, as well as the spectrum and the domain of corresponding operator are described.
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