DEGENERATE FIRST ORDER DIFFERENTIAL-OPERATOR EQUATIONS

Authors

  • L.P. Tepoyan Chair of Differential Equations, YSU, Armenia

DOI:

https://doi.org/10.46991/PYSU:A/2019.53.3.163

Keywords:

linear boundary value problems, spectral theory of linear operators

Abstract

We consider boundary value problem for degenerate first order differentialoperator equation $Lu \mathclose{\equiv} t^{\alpha} u^{\prime} \mathclose{-} P u \mathclose{=} f $, $ u(0) \mathclose{-} \mu u(b) \mathclose{=} 0 $, where $ t \mathclose{\in} (0,b) $,  $ a \mathclose{\geq} 0 $, $ P: H \mathclose{\rightarrow} H $ is linear operator in separable Hilbert space $ H $, $ f \mathclose{\in} L_{2, \beta} ((0,b),H) $,  $ \mu \mathclose{\in} \mathbb{C} $. We prove that under some conditions on the operator $ P $ and number $ \mu $ the boundary value problem has unique generalized solution $ u \mathclose{\in} L_{2, \beta} ((0,b),H) $ when $ 2 \alpha \mathclose{+} \beta \mathclose{<} 1 $,  $ \beta \mathclose{\geq} 0 $ and for any $ f \mathclose{\in} L_{2, \beta} ((0,b),H) $.

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Published

2019-12-16

How to Cite

Tepoyan, L. (2019). DEGENERATE FIRST ORDER DIFFERENTIAL-OPERATOR EQUATIONS. Proceedings of the YSU A: Physical and Mathematical Sciences, 53(3 (250), 163–169. https://doi.org/10.46991/PYSU:A/2019.53.3.163

Issue

Section

Mathematics