ON DEGENERATE NONSELF-ADJOINT DIFFERENTIAL EQUATIONS OF FOURTH ORDER

L.P. Tepoyan; H.S. Grigoryan

doi:10.46991/PYSU:A/2012.46.3.029

ON DEGENERATE NONSELF-ADJOINT DIFFERENTIAL EQUATIONS OF FOURTH ORDER

Authors

L.P. Tepoyan Chair of Differential Equations, YSU, Armenia
H.S. Grigoryan Chair of Differential Equations, YSU, Armenia

DOI:

https://doi.org/10.46991/PYSU:A/2012.46.3.029

Keywords:

Dirichlet problem, degenerate equations, weighted Sobolev spaces, spectral theory of linear operators

Abstract

We consider the degenerate nonself-adjoint differential equation of fourth order $Lu\equiv (t^{\alpha} u^{\prime\prime})^{\prime\prime} + au^{\prime\prime\prime} − pu^{\prime\prime} + qu = f$ , where $t \in(0, b), 0\leq\alpha\leq 2, \alpha ≠ 1,~a,~p,~q$ are the constant numbers and $a ≠ 0, p > 0, f \in L_2(0, b)$. We prove that the statement of the Dirichlet problem for the above equation depends on the sign of the number a (Keldysh Teorem).

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Published

2012-12-01

How to Cite

Tepoyan, L., & Grigoryan, H. (2012). ON DEGENERATE NONSELF-ADJOINT DIFFERENTIAL EQUATIONS OF FOURTH ORDER. Proceedings of the YSU A: Physical and Mathematical Sciences, 46(3 (229), 29–33. https://doi.org/10.46991/PYSU:A/2012.46.3.029