ON DEGENERATE NONSELF-ADJOINT DIFFERENTIAL EQUATIONS OF FOURTH ORDER

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Submitted: 2025-02-18; Published: 2025-02-18

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Abstract

We consider the degenerate nonself-adjoint differential equation of fourth order Lu≡(tαu′′)′′+au′′′−pu′′+qu=f , where t∈(0,b),0≤α≤2,α≠1, a, p, q are the constant numbers and a≠0,p>0,f∈L2(0,b). We prove that the statement of the Dirichlet problem for the above equation depends on the sign of the number a (Keldysh Teorem).