DEGENERATE DIFFERENTIAL-OPERATOR EQUATIONS ON INFINITE INTERVAL
DOI:
https://doi.org/10.46991/PYSU:A/2011.45.2.027Keywords:
Dirichlet problem, weighted Sobolev spaces, differential equations in abstract spaces, spectrum of the linear operatorAbstract
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.
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Published
2011-04-28
How to Cite
Ansari, H. (2011). DEGENERATE DIFFERENTIAL-OPERATOR EQUATIONS ON INFINITE INTERVAL. Proceedings of the YSU A: Physical and Mathematical Sciences, 45(2 (225), 27–32. https://doi.org/10.46991/PYSU:A/2011.45.2.027
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Mathematics
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