zbMATH — the first resource for mathematics

Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
On the oscillation of solutions of elliptic equations. (English. Russian original) Zbl 0615.35026
The author considers the equation $(-\Delta)\sp m u+a(x)u=0$, $a\in L\sb{\infty,loc}({\bbfR}\sp n)$, and calls this equation oscillatory if for each $r\sb 0>0$ there is some bounded domain G in the complement of the ball $\vert x\vert \le r\sb 0$ such that the equation has a nontrivial solution in the Sobolev space $\overset\circ\to W\sp m\sb 2(G)$. In the paper various conditions on a(x) -- in the form of pointwise or integral inequalities -- are given which imply oscillatory and nonoscillatory behaviour, respectively. The proofs consist in an estimation of the quadratic form associated with the equation.
Reviewer: F.Tomi

35J30Higher order elliptic equations, general
35B05Oscillation, zeros of solutions, mean value theorems, etc. (PDE)
35J40Higher order elliptic equations, boundary value problems