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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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