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Solvability of boundary value problems for operator-differential equations of mixed type: the degenerate case. (Russian, English) Zbl 1003.35040
Sib. Mat. Zh. 43, No. 3, 678-693 (2002); translation in Sib. Math. J. 43, No. 3, 549-561 (2002).
Boundary value problems in variable \(t\) are under study for operator-differential equations \(Bu_t - Lu = f\) (\(t\in (0,\infty)\)), where \(B\) and \(L\) are linear operators defined in a Hilbert space  \(E\). Operator \(B\) is not assumed to be invertible; in particular, \(B\) may have nontrivial kernel or the spectrum of \(B\) may contain infinite subsets of the positive and negative semiaxes simultaneously. To prove solvability of these boundary value problems, the authors study properties of solutions to the spectral problem \(Lu=\lambda Bu\).

MSC:
35G10 Initial value problems for linear higher-order PDEs
34G10 Linear differential equations in abstract spaces
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