DEGENERATE DIFFERENTIAL-OPERATOR EQUATIONS ON INFINITE INTERVAL

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.