ON DEGENERATE NONSELF-ADJOINT DIFFERENTIAL EQUATIONS OF FOURTH ORDER

Author(s)

ON DEGENERATE NONSELF-ADJOINT DIFFERENTIAL EQUATIONS OF FOURTH ORDER L.P. Tepoyan

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).

DOI: 10.46991/PYSUA.2012.46.3.029 Physical and Mathematical Sciences, 46(3 (229) 29-33

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Keywords

Dirichlet problem, degenerate equations, weighted Sobolev spaces, spectral theory of linear operators

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