Geodesic
A mixed problem for the fourth order degenerate ordinary differential equation
Proceedings of the Yerevan State University. Physical and mathematical sciences, no. 2 (2010), pp. 16-19.

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A mixed problem for the equation $Lu\equiv(t^{\alpha}u^{\prime\prime})^{\prime\prime}+au=f$ where $0\leq\alpha\leq 4$, $t\in[0,b]$, $f\in L_2(0,b)$ is considered. Firstly, the weighted Sobolev spaces $W_{\alpha}^2, W_{\alpha}^2(0), W_{\alpha}^2(b)$ and the generalized solution for the equation are defined. Next, the existence and uniqueness of the generalized solution for the mixed problem is studied, as well as the description of the spectrum of corresponding operator is given.
Keywords: mixed problem, weighted Sobolev spaces, generalized solution, spectrum of linear operators. 
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Esmail Yousefi. A mixed problem for the fourth order degenerate ordinary differential equation. Proceedings of the Yerevan State University. Physical and mathematical sciences, no. 2 (2010), pp. 16-19. http://geodesic.mathdoc.fr/item/UZERU_2010_2_a2/

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