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

Voir la notice de l'article provenant de la source Math-Net.Ru

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. 
@article{UZERU_2011_2_a4,
     author = {Hosein Ansari},
     title = {Degenerate differential-operator equations on infinite interval},
     journal = {Proceedings of the Yerevan State University. Physical and mathematical sciences},
     pages = {27--32},
     publisher = {mathdoc},
     number = {2},
     year = {2011},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/UZERU_2011_2_a4/}
}
TY  - JOUR
AU  - Hosein Ansari
TI  - Degenerate differential-operator equations on infinite interval
JO  - Proceedings of the Yerevan State University. Physical and mathematical sciences
PY  - 2011
SP  - 27
EP  - 32
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/UZERU_2011_2_a4/
LA  - en
ID  - UZERU_2011_2_a4
ER  - 
%0 Journal Article
%A Hosein Ansari
%T Degenerate differential-operator equations on infinite interval
%J Proceedings of the Yerevan State University. Physical and mathematical sciences
%D 2011
%P 27-32
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/UZERU_2011_2_a4/
%G en
%F UZERU_2011_2_a4
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/

[1] Proc. Steklov Inst. Math., 170 (1987), 185–218 | MR | Zbl | Zbl

[2] L.P. Tepoyan, Ansari Hosein, “Degenerate Ordinary Differential Equations of Fourth Order in Infinite Interval”, Vestnik RAU. Physical-Mathematical and Natural Sciences, 2010, no. 1, 3–10 (in Russian)

[3] Math. USSR-Sb., 43:3 (1982), 287–298 | DOI | MR | Zbl | Zbl

[4] L.P. Tepoyan, “Degenerate Fourth-Order Differential-Operator Equations”, Differential’nye Urawneniya, 23:8 (1987), 1366–1376 (in Russian) | MR | Zbl

[5] L.P. Tepoyan, “On a degenerate differential-operator equation”, Izv. NAN Armenii. Matematika, 34:5 (1999), 48–56 | MR | Zbl

[6] A.A. Dezin, Partial Differential Equations (An Introduction to a General Theory of Linear Boundary Value Problems), Springer, 1987 | MR | Zbl

[7] J. M. Berezanski, Expansion in Eigenfunctions of Selfadjoint Operators, Transl. Math. Monographs, 17, American Mathematical Society, Providence, 1968 | MR