NEUMANN PROBLEM FOR FOURTH ORDER DEGENERATE ORDINARY DIFFERENTIAL EQUATIONS

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Submitted: 2025-02-27; Published: 2025-02-27

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Abstract

In the present paper the Neumann problem for the equation Lu≡(tαuα)″+au+f, where 0≤α≤4, t∈[0,b], f∈L2(0,b) , is considered. Firstly, the weighted Sobolev space Wα2 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.