DEGENERATE DIFFERENTIAL-OPERATOR EQUATIONS ON INFINITE INTERVAL

Author(s)

DEGENERATE DIFFERENTIAL-OPERATOR EQUATIONS ON INFINITE INTERVAL Hosein Ansari

In the present paper we consider the Dirichlet problem for the fourth order differential-operator equation Lu≡(tαu′′)′′+t−2Au=f , where t∈(1,+∞),α≥2,f∈L2,2((1,+∞),H), A is a linear operator in the separable Hilbert space H and has a complete system of eigenvectors that form a Riesz basis in H. The existence and uniqueness of the generalized solution for the Dirichlet problem are proved, and the description of spectrum for the corresponding operator is given.

DOI: 10.46991/PYSUA.2011.45.2.027 Physical and Mathematical Sciences, 45(2 (225) 27-32

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Keywords

Dirichlet problem, weighted Sobolev spaces, differential equations in abstract spaces, spectrum of the linear operator

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