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)
Limit circle/limit point criteria for second-order sublinear differential equations with damping term. (English) Zbl 1272.34034
Consider the scalar equation $$(a(t)y')'+ b(t)y'+ r(t) y^\gamma= 0,\tag{$*$}$$ where $a,r: \Bbb R_+\to \Bbb R$ are sufficiently smooth, $b: \Bbb R_+\to\Bbb R_+$ is continuous, $\gamma= 2k-1$ with $k= (M+ N- 1)/(2N- 1)$, where $M$ and $N$ are positive integers. The authors present necessary and sufficient conditions for $(*)$ to be of limit-circle type or limit-point type.

34B20Weyl theory and its generalizations
Full Text: DOI
[1] H. Weyl, “Über gewöhnliche Differentialgleichungen mit Singularitäten und die zugehörigen Entwicklungen willkürlicher Funktionen,” Mathematische Annalen, vol. 68, no. 2, pp. 220-269, 1910. · Zbl 41.0343.01 · doi:10.1007/BF01474161
[2] M. Bartusek, Z. Dosla, and J. R. Graef, “On the definitions of the nonlinear limitpoint/limit-circle properties,” Differential Equations and Dynamical Systems, vol. 9, pp. 49-61, 2001. · Zbl 1231.34044
[3] M. Bartu\vsek and J. R. Graef, “Some limit-point and limit-circle results for second order Emden-Fowler equations,” Applicable Analysis, vol. 83, no. 5, pp. 461-476, 2004. · Zbl 1053.34024 · doi:10.1080/00036810310001632835
[4] J. R. Graef, “Limit circle type criteria for nonlinear differential equations,” Proceedings of the Japan Academy, Series A, vol. 55, no. 2, pp. 49-52, 1979. · Zbl 0428.34017 · doi:10.3792/pjaa.55.49
[5] J. R. Graef, “Limit circle criteria and related properties for nonlinear equations,” Journal of Differential Equations, vol. 35, no. 3, pp. 319-338, 1980. · Zbl 0441.34024 · doi:10.1016/0022-0396(80)90032-7
[6] J. R. Graef and P. W. Spikes, “On the nonlinear limit-point/limit-circle problem,” Nonlinear Analysis, vol. 7, no. 8, pp. 851-871, 1983. · Zbl 0535.34023 · doi:10.1016/0362-546X(83)90062-7
[7] P. W. Spikes, “Criteria of limit circle type for nonlinear differential equations,” SIAM Journal on Mathematical Analysis, vol. 10, no. 3, pp. 456-462, 1979. · Zbl 0413.34033 · doi:10.1137/0510042
[8] M. V. Fedoryuk, Asymptotic Analysis, Springer, New York, NY, USA, 1993. · Zbl 0782.34001
[9] P. Hartman and A. Wintner, “Criteria of non-degeneracy for the wave equation,” American Journal of Mathematics, vol. 70, pp. 295-308, 1948. · Zbl 0035.18201 · doi:10.2307/2372327
[10] M. Bartu\vsek, Z. Do\vslá, and J. R. Graef, The Nonlinear Limit-Point/Limit-Circle Problem, Birkhäuser, Boston, Mass, USA, 2005.