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.
No institution available
Mathematics
, 2025, Issue 1, pp. 1–10
ISSN Online: 0000-0000
DOI:
10.xxxx/example-doi