Natural Sciences, Mathematics, 2026
DEGENERATE DIFFERENTIAL-OPERATOR EQUATIONS ON INFINITE INTERVAL
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Submitted: 2025-02-22
© 2026 by author(s) and The Gufo Inc.
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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.