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 t^α u^′ - P u = f , u(0) - μ u(b) = 0 , where t (0,b) , a ≥ 0 , P: H → H is linear operator in separable Hilbert space H , f L_2, β ((0,b),H) , μ C . We prove that under some conditions on the operator P and number μ the boundary value problem has unique generalized solution u L_2, β ((0,b),H) when 2 α + β < 1 , β ≥ 0 and for any f L_2, β ((0,b),H) .