2012; Physical and Mathematical Sciences, 46(3 (229): 29–33
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ON DEGENERATE NONSELF-ADJOINT DIFFERENTIAL EQUATIONS OF FOURTH ORDER

L.P. Tepoyan*

Received: 2025-02-18 · Published: 2012-12-01

© 2012 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
ON DEGENERATE NONSELF-ADJOINT DIFFERENTIAL EQUATIONS OF FOURTH ORDER
Author
L.P. Tepoyan
Published
2012-12-01
Licence
Creative Commons Attribution 4.0 International

Abstract

We consider the degenerate nonself-adjoint differential equation of fourth order Lu≡(tαu′′)′′+au′′′−pu′′+qu=f , where t∈(0,b),0≤α≤2,α≠1, a, p, q are the constant numbers and a≠0,p>0,f∈L2(0,b). We prove that the statement of the Dirichlet problem for the above equation depends on the sign of the number a (Keldysh Teorem).
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