Natural Science, Mathematics, 2025
DEGENERATE DIFFERENTIAL-OPERATOR EQUATIONS ON INFINITE INTERVAL
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Submitted: 2025-02-22; Published: 2025-02-22
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Abstract
In the present paper we consider the Dirichlet problem for the fourth order differential-operator equationĀ Luā”(tĪ±uā²ā²)ā²ā²+tā2Au=fĀ , whereĀ tā(1,+ā),Ī±ā„2,fāL2,2((1,+ā),H),Ā AĀ is a linear operator in the separable Hilbert spaceĀ HĀ and has a complete system of eigenvectors that form a Riesz basis inĀ 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.