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 three positive solutions to a second-order boundary value problem on a measure chain. (English) Zbl 1032.39009
The authors use the so called “five functionals fixed point theorem”, a generalization of the Leggett-Williams fixed point theorem, in order to prove the existence of at least three positive solutions of a boundary value problem. This boundary value problem consists of a second order dynamic equation on a measure chain/time scale and a Sturm-Liouville type boundary condition.

MSC:
39A12Discrete version of topics in analysis
93C70Time-scale analysis and singular perturbations
34B24Sturm-Liouville theory
39A11Stability of difference equations (MSC2000)
WorldCat.org
Full Text: DOI
References:
[1] Agarwal, R. P.; Bohner, M.: Basic calculus on time scales and some of its applications. Results math. 35, 3-22 (1999) · Zbl 0927.39003
[2] Agarwal, R. P.; O’regan, D.; Wong, P. J. Y.: Positive solutions of differential, difference and integral equations. (1999)
[3] Anderson, D.; Avery, R. I.; Peterson, A. C.: Three positive solutions to a discrete focal boundary value problem. J. comput. Appl. math. 88, 103-118 (1998) · Zbl 1001.39021
[4] Anderson, D.; Avery, R. I.: Multiple positive solutions to a third order discrete focal boundary value problem. Comput. math., appl. 42, 333-340 (2001) · Zbl 1001.39022
[5] B. Aulbach, S. Hilger, Linear dynamic processes with inhomogeneous time scale, in: Nonlinear Dynamics and Quantum Dynamical Systems, Mathematical Research, vol. 59, Akademie Verlag, Berlin, 1990. · Zbl 0719.34088
[6] R.I. Avery, Multiple Positive Solutions to Boundary Value Problems, Dissertation, University of Nebraska-Lincoln, 1997.
[7] Avery, R. I.: A generalization of the Leggett-Williams fixed point theorem. MSR hot-line 2, 9-14 (1998) · Zbl 0965.47038
[8] Avery, R. I.: Multiple positive solutions of an nth order focal boundary value problem. Panamer. math. J. 8, 39-55 (1998) · Zbl 0960.34015
[9] Avery, R. I.; Peterson, A. C.: Multiple positive solutions of a discrete second order conjugate problem. Panamer. math. J. 8, 1-12 (1998) · Zbl 0959.39006
[10] Chyan, C. J.; Henderson, J.: Eigenvalue problems for nonlinear differential equations on a measure chain. J. math. Anal. appl. 245, No. 2, 547-559 (2000) · Zbl 0953.34068
[11] Chyan, C. J.; Henderson, J.: Positive solutions in an annulus for nonlinear differential equations on a measure chain. Tamkang J. Math. 30 (1999) · Zbl 0995.34017
[12] Chyan, C. J.; Henderson, J.: Multiple solutions for 2mth order Sturm-Liouville boundary value problems. Comput. math. Appl. 40, 231-237 (2000) · Zbl 0958.34018
[13] Davis, J. M.; Erbe, L. H.; Henderson, J.: Multiplicity of positive solutions for higher order Sturm-Liouville problems. Rocky mountain J. Math. 21, 169-184 (2001) · Zbl 0989.34012
[14] Deimling, K.: Nonlinear functional analysis. (1985) · Zbl 0559.47040
[15] Erbe, L. H.; Hilger, S.: Sturmian theory on measure chains. Differential equations dynamics systems 1, 223-246 (1993) · Zbl 0868.39007
[16] Erbe, L. H.; Hu, S.; Wang, H.: Multiple positive solutions of some boundary value problems. J. math. Anal. appl. 184, 640-648 (1994) · Zbl 0805.34021
[17] Erbe, L. H.; Peterson, A.: Positive solutions for a nonlinear differential equation on a measure chain. Math. comput. Modelling 32, 571-585 (2000) · Zbl 0963.34020
[18] Erbe, L. H.; Peterson, A.: Green’s functions and comparison theorems for differential equations on measure chains. Dynamics continuous, discrete impulsive systems 6, 121-137 (1999) · Zbl 0938.34027
[19] Erbe, L. H.; Peterson, A.: Eigenvalue conditions and positive solutions. J. differ. Equations appl. 6, 165-191 (2000) · Zbl 0949.34015
[20] Erbe, L. H.; Tang, M.: Existence and multiplicity of positive solutions to nonlinear boundary value problems. Diff. eqns. Dynam. sys. 4, 313-320 (1996) · Zbl 0868.35035
[21] Erbe, L. H.; Wang, H.: On the existence of positive solutions of ordinary differential equations. Proc. amer. Math. soc. 120, 743-748 (1994) · Zbl 0802.34018
[22] Guo, D.; Lakshmikantham, V.: Nonlinear problems in abstract cones. (1988) · Zbl 0661.47045
[23] Henderson, J.: Multiple solutions for 2mth order Sturm-Liouville boundary value problems on a measure chain. J. difference equations appl. 6, 417-429 (2000) · Zbl 0965.39008
[24] Hilger, S.: Analysis on a measure chain--a unified approach to continuous and discrete calculus. Resultate math. 18, 18-56 (1990) · Zbl 0722.39001
[25] Krasnosel’skii, M. A.: Positive solutions of operator equations. (1964)
[26] Leggett, R. W.; Williams, L. R.: Multiple positive fixed points of nonlinear operators on ordered Banach spaces. Indiana univ. Math. J. 28, 673-688 (1979) · Zbl 0421.47033
[27] Wang, H.: On the existence of positive solutions for semilinear elliptic equations in the annulus. J. differential equations 109, 1-7 (1994) · Zbl 0798.34030