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 and uniqueness results for discrete second-order periodic boundary value problems. (English) Zbl 1057.39008
The paper contains results on existence and uniqueness of a second order nonlinear difference equation $$ - \Delta^2 y(n-1) + q(n) y(n) = f(n,y(n)), $$ $\Delta$ the forward difference operator, with periodic boundary conditions. The methods used in the proofs are based on the notions of lower and upper solutions, Green’s functions and Brouwer’s fixed point theorem.

MSC:
39A12Discrete version of topics in analysis
34B15Nonlinear boundary value problems for ODE
39A11Stability of difference equations (MSC2000)
WorldCat.org
Full Text: DOI
References:
[1] Agarwal, R. P.; O’regan, D.: Boundary value problems for discrete equations. Appl. math. Lett. 10, No. 4, 83-89 (1997) · Zbl 0890.39001
[2] Agarwal, R. P.; Wong, P. J. Y.: Advanced topics in difference equations. (1997) · Zbl 0878.39001
[3] Atici, F. M.; Guseinov, G. Sh.: Positive periodic solutions for nonlinear difference equations with periodic coefficients. J. math. Anal. appl. 232, 166-182 (1999) · Zbl 0923.39010
[4] Cabada, A.: Extremal solutions for the difference ${\phi}$-Laplacian problem with nonlinear functional boundary conditions. Computers math. Applic. 42, 593-601 (2001) · Zbl 1001.39006
[5] Cabada, A.: The method of lower and upper solutions for second, third, fourth, and higher order boundary value problems. J. math. Anal. app. 185, 302-320 (1994) · Zbl 0807.34023
[6] Cabada, A.; Nieto, J. J.: A generalization of the monotone iterative technique for nonlinear second order periodic boundary value problems. J. math. Anal. app. 151, 181-189 (1990) · Zbl 0719.34039
[7] Cabada, A.; Otero-Espinar, V.: Optimal existence results for nth order periodic boundary value difference problems. J. math. Anal. app. 247, 67-86 (2000) · Zbl 0962.39006
[8] Zhuang, W.; Chen, Y.; Cheng, S. S.: Monotone methods for a discrete boundary problem. Computers math. Applic. 32, No. 12, 41-49 (1996) · Zbl 0872.39005
[9] Hristova, S. G.; Roberts, L. F.: Monotone-iterative method of V. Lakshmikantham for a periodic boundary value problem for a class of differential equations with ”supremum”. Nonlinear anal. 44, 601-612 (2001) · Zbl 1003.34023
[10] Heikkilä, S.; Lakshmikantham, V.: Monotone iterative techniques for discontinuous nonlinear differential equations. (1994) · Zbl 0804.34001
[11] Kannan, R.; Lakshmikantham, V.: Existence of periodic solutions of nonlinear boundary value problems and the method of upper and lower solutions. App. anal. 17, 103-113 (1984) · Zbl 0532.34030
[12] Lakshmikantham, V.; Leela, S.: Remarks on first and second order periodic boundary value problems. Nonlinear anal. 8, 281-287 (1984) · Zbl 0532.34029
[13] Leela, S.: Monotone method for second order periodic boundary value problems. Nonlinear anal. 7, 349-355 (1983) · Zbl 0524.34023
[14] Nieto, J. J.: Nonlinear second-order periodic boundary value problems. J. math. Anal. appl. 130, 22-29 (1988) · Zbl 0678.34022
[15] Sedziwy, S.: Nonlinear periodic boundary value problem for a second order ordinary differential equations. Nonlinear anal. 32, No. 7, 881-890 (1998)
[16] Ma, R.: Multiplicity of positive solutions for second-order three-point boundary value problems. Computers math. Applic. 40, No. 2/3, 193-204 (2000) · Zbl 0958.34019
[17] Nieto, J. J.: An abstract monotone iterative technique. Nonlinear anal. 28, No. 12, 1923-1933 (1997) · Zbl 0883.47058
[18] Pao, C. V.: Monotone iterative methods for finite difference system of reaction-diffusion equations. Numer. math. 46, 571-586 (1985) · Zbl 0589.65072
[19] Wang, Y. M.: Monotone methods for a boundary value problem of second-order discrete equation. Computers math. Applic. 36, No. 6, 77-92 (1998) · Zbl 0932.65130
[20] Agarwal, R. P.: Boundary value problems for higher order differential equations. (1986) · Zbl 0619.34019
[21] Kelley, W. G.; Peterson, A. C.: Difference equations: an introduction with applications. (1991) · Zbl 0733.39001
[22] Dunford, N.; Schwartz, J.: Linear operators, (Part I). (1957) · Zbl 0128.34803