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)
Exact solutions of a class of second-order nonlocal boundary value problems and applications. (English) Zbl 1189.34005

The author considers the second-order linear differential equation

-u '' +k 2 u=f(t),t[a,b]

subject to different multipoint boundary conditions. He presents the exact solution by means of Green’s function. As applications he studies uniqueness and iteration of the positive solutions for a nonlinear singular second-order m-point boundary value problem.

34A05Methods of solution of ODE
34B05Linear boundary value problems for ODE
34B10Nonlocal and multipoint boundary value problems for ODE
34B27Green functions
34A45Theoretical approximation of solutions of ODE
34B18Positive solutions of nonlinear boundary value problems for ODE
[1]Pokornyi, Yu V.; Borovskikh, A. V.: The connection of the Green’s function and the influence function for nonclassical problems, Journal of mathematical sciences 119, No. 6, 739-768 (2004) · Zbl 1079.34016 · doi:10.1023/B:JOTH.0000012754.03115.4f
[2]Zhao, Zengqin: Solutions and greens functions for some linear second-order three-point boundary value problems, Computers and mathematics with applications 56, 104-113 (2008) · Zbl 1145.34324 · doi:10.1016/j.camwa.2007.11.037
[3]Bai, Chuanzhi; Xie, Dapeng; Liu, Yang; Wang, Chunli: Positive solutions for second-order four-point boundary value problems with alternating coefficient, Nonlinear analysis 70, 2014-2023 (2009) · Zbl 1173.34012 · doi:10.1016/j.na.2008.02.099
[4]Chen, Haibo; Li, Peiluan: Three-point boundary value problems for second-order ordinary differential equations in Banach spaces, Computers and mathematics with applications 56, 1852-1860 (2008) · Zbl 1152.34362 · doi:10.1016/j.camwa.2008.04.024
[5]Han, Xiaoling: Positive solutions for a three-point boundary value problem at resonance, Journal of mathematical analysis and applications 336, 556-568 (2007) · Zbl 1125.34014 · doi:10.1016/j.jmaa.2007.02.069
[6]Liu, Xiping; Jia, Mei: Existence of monotone positive solutions to a type of three-point boundary value problem, Acta mathematicae applicatae sinica 30, No. 1, 111-119 (2007) · Zbl 1125.34008
[7]Pang, Huihui; Feng, Meiqiang; Ge, Weigao: Existence and monotone iteration of positive solutions for a three-point boundary value problem, Applied mathematics letters 21, 656-661 (2008) · Zbl 1152.34313 · doi:10.1016/j.aml.2007.07.019
[8]Sun, Jingxian; Xu, Xian; Donal, O’regan: Nodal solutions for m-point boundary value problems using bifurcation methods, Nonlinear analysis 68, 3034-3046 (2008) · Zbl 1141.34009 · doi:10.1016/j.na.2007.02.043
[9]Zhang, Kemei; Xie, Xue-Jun: Existence of sign-changing solutions for some asymptotically linear three-point boundary value problems, Nonlinear analysis 70, 2796-2805 (2009) · Zbl 1165.34005 · doi:10.1016/j.na.2008.04.004
[10]Feng, Hanying; Ge, Weigao; Jiang, Ming: Multiple positive solutions for m-point boundary-value problems with a one-dimensional p-Laplacian, Nonlinear analysis 68, 2269-2279 (2008) · Zbl 1138.34005 · doi:10.1016/j.na.2007.01.052
[11]Feng, Meiqiang; Zhang, Xuemei; Ge, Weigao: Exact number of solutions for a class of two-point boundary value problems with one-dimensional p-Laplacian, Journal of mathematical analysis and applications 338, 784-792 (2008) · Zbl 1147.34008 · doi:10.1016/j.jmaa.2007.04.058
[12]Guo, Yanping; Ji, Yude; Liu, Xiujun: Multiple positive solutions for some multi-point boundary value problems with p-Laplacian, Journal of computational and applied mathematics 216, 144-156 (2008) · Zbl 1141.34017 · doi:10.1016/j.cam.2007.04.023
[13]Ji, Dehong; Ge, Weigao: Existence of multiple positive solutions for Sturm – Liouville-like four-point boundary value problem with p-Laplacian, Nonlinear analysis 68, 2638-2646 (2008) · Zbl 1145.34309 · doi:10.1016/j.na.2007.02.010
[14]Lian, Hairong; Ge, Weigao: Positive solutions for a four-point boundary value problem with the p-Laplacian, Nonlinear analysis 68, 3493-3503 (2008) · Zbl 1151.34019 · doi:10.1016/j.na.2007.03.042
[15]Xu, Fuyi: Multiple positive solutions for nonlinear singular m-point boundary value problem, Applied mathematics and computation 204, 450-460 (2008) · Zbl 1159.34018 · doi:10.1016/j.amc.2008.05.139
[16]Zhu, Yanling; Wang, Kai: On the existence of solutions of p-Laplacian m-point boundary value problem at resonance, Nonlinear analysis 70, 1557-1564 (2009) · Zbl 1165.34314 · doi:10.1016/j.na.2008.02.035