DEGENERATE FIRST ORDER DIFFERENTIAL-OPERATOR EQUATIONS - Tepoyan, L.P. (Proceedings of the YSU A: Physical and Mathematical Sciences, 2019)
We consider boundary value problem for degenerate first order differentialoperator equation $Lu \mathclose{\equiv} t^{α} u^{′} \mathclose{-} P u \mathclose{=} f $, $ u(0) \mathclose{-} μ u(b) \mathclose{=} 0 $, where $ t \mathclose{\in} (0,b) $, $ a \mathclose{≥} 0 $, $ P: H \mathclose{→} H $ is linear operator in separable Hilbert space $ H $, $ f \mathclose{\in} L_{2, β} ((0,b),H) $, $ μ \mathclose{\in} \mathbb{C} $. We prove that under some conditions on the operator $ P $ and number $ μ $ the boundary value problem has unique generalized solution $ u \mathclose{\in} L_{2, β} ((0,b),H) $ when $ 2 α \mathclose{+} β \mathclose{
Keywords: linear boundary value problems; spectral theory of linear operators