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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

##### MSC:
 34B10 Nonlocal and multipoint boundary value problems for ordinary differential equations
##### Keywords:
set of eigenvalues; spectrum