NEUMANN PROBLEM FOR FOURTH ORDER DEGENERATE ORDINARY DIFFERENTIAL EQUATIONS - Tepoyan, L. P.; Kalvand, Daryoush (Proceedings of the YSU A: Physical and Mathematical Sciences, 2010)
In the present paper the Neumann problem for the equation $Lu \equiv (t^α u^α)''+ au +f,$ where $0≤ α≤ 4,~t\in[0, b],~f\in L_2(0, b)$ , is considered. Firstly, the weighted Sobolev space $W^2_α$ and generalized solution for the abovementioned equation are defined. Then, the existence and uniqueness of the generalized solution is studied, as well as the spectrum and the domain of corresponding operator are described.
Keywords: Neumann problem; weighted Sobolev spaces; generalized solution; spectrum of linear operators