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)
The positive properties of the Green function for Dirichlet-type boundary value problems of nonlinear fractional differential equations and its application. (English) Zbl 1192.34008
The authors discuss some new positive properties of the Green function for boundary value problems of nonlinear Dirichlet-type fractional differential equation $$\align &D_{0^+}^{\alpha}u(t)+f(t,u(t))=0,\quad 0<t<1,\\ &u(0)=u(1)=0 \endalign$$ Applications are also given.

34A08Fractional differential equations
34B27Green functions
47N20Applications of operator theory to differential and integral equations
34B15Nonlinear boundary value problems for ODE
Full Text: DOI
[1] Agrawal, O. P.: Formulation of Euler--Lagrange equations for fractional variational problems, J. math. Anal. appl. 272, 368-379 (2002) · Zbl 1070.49013 · doi:10.1016/S0022-247X(02)00180-4
[2] Delbosco, D.; Rodino, L.: Existence and uniqueness for a nonlinear fractional differential equation, J. math. Appl. 204, 609-625 (1996) · Zbl 0881.34005 · doi:10.1006/jmaa.1996.0456
[3] Leggett, R. W.; Williams, L. R.: Multiple positive solutions of nonlinear operators on ordered Banach spaces, Indiana univ. Math. J. 28, 673-688 (1979) · Zbl 0421.47033 · doi:10.1512/iumj.1979.28.28046
[4] Podlubny, I.: Fractional differential equations, Mathematics in science and engineering 198 (1999) · Zbl 0924.34008
[5] Samko, S. G.; Kilbas, A. A.; Marichev, O. I.: Fractional integral and derivatives (Theory and applications), (1993) · Zbl 0818.26003
[6] Bai, Zhanbing; Lü, Haishen: 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
[7] Zhang, Shu-Qin: The existence of a positive solution for a nonlinear fractional differential equation, J. math. Anal. appl. 252, 804-812 (2000) · Zbl 0972.34004 · doi:10.1006/jmaa.2000.7123
[8] Zhang, Shu-Qin: Existence of positive solution for some class of nonlinear fractional differential equations, J. math. Anal. appl. 278, No. 1, 136-148 (2003) · Zbl 1026.34008 · doi:10.1016/S0022-247X(02)00583-8
[9] Wei, Zhongli: Positive solution of singular Dirichlet boundary value problems for second order differential equation system, J. math. Anal. appl. 328, 1255-1267 (2007) · Zbl 1115.34025 · doi:10.1016/j.jmaa.2006.06.053
[10] Zhang, Xinguang; Liu, Lishan; Wu, Yonghong: Positive solutions of nonresonance semipositone singular Dirichlet boundary value problems, Nonlinear anal. TMA 68, No. 1, 97-108 (2008) · Zbl 1135.34016 · doi:10.1016/j.na.2006.10.034
[11] Agarwal, Ravi P.; O’regan, Donal: Twin solutions to singular Dirichlet problems, J. math. Anal. appl. 240, No. 2, 433-445 (1999) · Zbl 0946.34022 · doi:10.1006/jmaa.1999.6597
[12] Tersenov, Alkis S.; Tersenov, Aris S.: The problem of Dirichlet for evolution one-dimensional p-Laplacian with nonlinear source, J. math. Anal. appl. 340, 1109-1119 (2008) · Zbl 1137.35386 · doi:10.1016/j.jmaa.2007.09.020
[13] Lin, Xiaoning; Jiang, Daqing: Multiple positive solutions of Dirichlet boundary value problems for second order impulsive differential equations, J. math. Anal. appl. 321, No. 2, 501-514 (2006) · Zbl 1103.34015 · doi:10.1016/j.jmaa.2005.07.076
[14] O’regan, Donal: Singular Dirichlet boundary value problems. Superlinear and nonresonant case, Nonlinear anal. 29, No. 2, 221-245 (1997) · Zbl 0884.34028 · doi:10.1016/S0362-546X(96)00026-0
[15] Krasnosel’skii, M. A.: Positive solutions of operator equations, (1964) · Zbl 0121.10604
[16] Lakshmikantham, V.; Vatsala, A. S.: Theory of fractional differential inequalities and applications, Commun. appl. Anal. 11, No. 3--4, 395-402 (2007) · Zbl 1159.34006
[17] Lakshmikantham, V.; Vatsala, A. S.: General uniqueness and monotone iterative technique for fractional differential equations, Appl. math. Lett. 21, 828-834 (2008) · Zbl 1161.34031 · doi:10.1016/j.aml.2007.09.006
[18] Lakshmikantham, V.; Vatsala, A. S.: Basic theory of fractional differential equations, Nonlinear anal. TMA 69, No. 8, 2677-2682 (2008) · Zbl 1161.34001 · doi:10.1016/j.na.2007.08.042