DEGENERATE FIRST ORDER DIFFERENTIAL-OPERATOR EQUATIONS

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DEGENERATE FIRST ORDER DIFFERENTIAL-OPERATOR EQUATIONS Tepoyan Tepoyan

We consider boundary value problem for degenerate first order differential-operator equationLu≡tαu′−Pu=f,u(0)−μu(b) =0,wheret∈(0,b),α≥0,P:H→His linear operator in separable Hilbert spaceH,f∈L2,β((0,b),H),μ∈C. We prove that under some conditions on the operatorPand numberμthe boundary value problem has unique generalized solutionu∈L2,β((0,b),H)when 2α+β<1,β≥0 and for anyf∈L2,β((0,b),H).

DOI: 10.46991/PYSU:A/2019.53.3.163 Physical and Mathematical Sciences, 53(3 (250) 163-169

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Keywords

linear boundary value problems, spectral theory of linear operators

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