2011; Physical and Mathematical Sciences, 45(2 (225): 27–32
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DEGENERATE DIFFERENTIAL-OPERATOR EQUATIONS ON INFINITE INTERVAL

Hosein Ansari*

Received: 2025-02-22 · Published: 2011-04-28

© 2011 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
DEGENERATE DIFFERENTIAL-OPERATOR EQUATIONS ON INFINITE INTERVAL
Author
Hosein Ansari
Published
2011-04-28
Licence
Creative Commons Attribution 4.0 International

Abstract

In the present paper we consider the Dirichlet problem for the fourth order differential-operator equation Lu≡(tαu′′)′′+t−2Au=f , where t∈(1,+∞),α≥2,f∈L2,2((1,+∞),H), A is a linear operator in the separable Hilbert space H and has a complete system of eigenvectors that form a Riesz basis in H. The existence and uniqueness of the generalized solution for the Dirichlet problem are proved, and the description of spectrum for the corresponding operator is given.
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