zbMATH — the first resource for mathematics

Examples
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.

Operators
a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
Fields
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)
Existence of a positive solution to a class of fractional differential equations. (English) Zbl 1204.34007
The author considers a class of fractional boundary value problem involving the Riemann-Liouville derivative. The main contribution of the author is to improve certain recent results by showing that the Green function associated to the mentioned problem satisfies, among other properties, a Harnack-like inequality. Also, the author shows that the mentioned boundary problem has a positive solution under standard assumptions on the nonlinearity part of the fractional differential equation.
MSC:
34A08Fractional differential equations
34B15Nonlinear boundary value problems for ODE
34B18Positive solutions of nonlinear boundary value problems for ODE
References:
[1]Bai, Z.; Lü, H.: Positive solutions for boundary value problem of nonlinear fractional differential equation, J. math. Anal. appl. 311, 495-505 (2005) · Zbl 1079.34048 · doi:10.1016/j.jmaa.2005.02.052
[2]Xu, X.; Jiang, D.; Yuan, C.: Multiple positive solutions for the boundary value problem of a nonlinear fractional differential equation, Nonlinear anal. TMA 71, 4676-4688 (2009) · Zbl 1178.34006 · doi:10.1016/j.na.2009.03.030
[3], Reviews of nonlinear dynamics and complexity (2008)
[4]Lakshmikantham, V.; Vatsala, A. S.: Basic theory of fractional differential equations, Nonlinear anal. TMA 69, 2677-2682 (2008) · Zbl 1161.34001 · doi:10.1016/j.na.2007.08.042
[5]Zhang, S.: Positive solutions to singular boundary value problem for nonlinear fractional differential equation, Comput. math. Appl. 59, 1300-1309 (2010) · Zbl 1189.34050 · doi:10.1016/j.camwa.2009.06.034
[6]Erbe, L. H.; Wang, H.: On the existence of positive solutions of ordinary differential equations, Proc. amer. Math. soc. 120, No. 3, 743-748 (1994) · Zbl 0802.34018 · doi:10.2307/2160465
[7]Davis, J. H.; Henderson, J.: Triple positive solutions for (k,n-k) conjugate boundary value problems, Math. slovaca 51, No. 3, 313-320 (2001) · Zbl 0996.34017
[8]Graef, J. R.; Yang, B.: Positive solutions of a nonlinear fourth order boundary value problem, Comm. appl. Nonlinear anal. 14, No. 1, 61-73 (2007) · Zbl 1136.34024
[9]Ma, R.; Xu, L.: Existence of positive solutions of a nonlinear fourth-order boundary value problem, Appl. math. Lett. 23, No. 5, 537-543 (2010) · Zbl 1195.34037 · doi:10.1016/j.aml.2010.01.007
[10]Podlubny, I.: Fractional differential equations, (1999)
[11]Agarwal, R.; Meehan, M.; O’regan, D.: Fixed point theory and applications, (2001)