Geodesic
Degenerate differential-operator equations on infinite interval
Proceedings of the Yerevan State University. Physical and mathematical sciences, no. 2 (2011), pp. 27-32

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In the present paper we consider the Dirichlet problem for the fourth order differential-operator equation $Lu\equiv(t^{\alpha}u^{\prime\prime})^{\prime\prime}+t^{-2}Au=f,$ where $t\in(1,~ +\infty),~\alpha\geq 2,~f\in L_{2,2}((1,~ +\infty),H),$ $A$ 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.
Keywords: Dirichlet problem, weighted Sobolev spaces, differential equations in abstract spaces, spectrum of the linear operator. 
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Hosein Ansari. Degenerate differential-operator equations on infinite interval. Proceedings of the Yerevan State University. Physical and mathematical sciences, no. 2 (2011), pp. 27-32. http://geodesic.mathdoc.fr/item/UZERU_2011_2_a4/