DEGENERATE FIRST ORDER DIFFERENTIAL-OPERATOR EQUATIONS

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Submitted: 2025-01-29; Published: 2025-01-29

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Abstract

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).