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On the spectrum of a multipoint boundary value problem. (Russian) Zbl 0562.34009
The author investigates the set of eigenvalues \(\lambda\) for the problem \[ x^{(n)}(t)+\sum^{n}_{k=1}f_ k(t)x^{(n-k)}(t)=\lambda [x^{(p)}(t)+\sum^{q}_{j=1}g_ j(t)x^{(p-j)}(t)] \] for \(t\in I:=[0,1].\)
x\({}^{(k)}(a_ i)=0\) for \(k=0,...,r_ i-1\), \(i=1,...,m\), where \(\sum^{m}_{i=1}r_ i=n\) and \(0=a_ 1<a_ 2<...<a_ m=1\). For continuous functions \(f_ k\), \(g_ j\) on I and \(p<n-2\) and under some additional assumptions the author establishes a condition equivalent to the finiteness of the spectrum. When the condition is not satisfied then the spectrum is countable and asymptotic formulas for \(\lambda\) are given. There are no proofs.
Reviewer: J.Kalinowski

34B10 Nonlocal and multipoint boundary value problems for ordinary differential equations