Multipoint boundary value problems for discrete equations

Pavel Drábek; Harold Bevan Thompson; Christopher Tisdell

Commentationes Mathematicae Universitatis Carolinae (2001)

  • Volume: 42, Issue: 3, page 459-468
  • ISSN: 0010-2628

Abstract

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In this work we establish existence results for solutions to multipoint boundary value problems for second order difference equations with fully nonlinear boundary conditions involving two, three and four points. Our results are also applied to systems.

How to cite

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Drábek, Pavel, Thompson, Harold Bevan, and Tisdell, Christopher. "Multipoint boundary value problems for discrete equations." Commentationes Mathematicae Universitatis Carolinae 42.3 (2001): 459-468. <http://eudml.org/doc/248779>.

@article{Drábek2001,
abstract = {In this work we establish existence results for solutions to multipoint boundary value problems for second order difference equations with fully nonlinear boundary conditions involving two, three and four points. Our results are also applied to systems.},
author = {Drábek, Pavel, Thompson, Harold Bevan, Tisdell, Christopher},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {second order difference equations; discrete boundary value problems; multipoint boundary conditions; degree theory; nonlinear boundary conditions; second order difference equations; discrete boundary value problems; multipoint boundary conditions; degree theory; nonlinear boundary conditions},
language = {eng},
number = {3},
pages = {459-468},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Multipoint boundary value problems for discrete equations},
url = {http://eudml.org/doc/248779},
volume = {42},
year = {2001},
}

TY - JOUR
AU - Drábek, Pavel
AU - Thompson, Harold Bevan
AU - Tisdell, Christopher
TI - Multipoint boundary value problems for discrete equations
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2001
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 42
IS - 3
SP - 459
EP - 468
AB - In this work we establish existence results for solutions to multipoint boundary value problems for second order difference equations with fully nonlinear boundary conditions involving two, three and four points. Our results are also applied to systems.
LA - eng
KW - second order difference equations; discrete boundary value problems; multipoint boundary conditions; degree theory; nonlinear boundary conditions; second order difference equations; discrete boundary value problems; multipoint boundary conditions; degree theory; nonlinear boundary conditions
UR - http://eudml.org/doc/248779
ER -

References

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  2. Agarwal R.P., On boundary value problems for second order discrete systems, Appl. Anal. 20 (1985), 1-17. (1985) Zbl0596.39003MR0808054
  3. Agarwal R.P., Difference Equations and Inequalities, Marcel Dekker, New York, 1992. Zbl0952.39001MR1155840
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  7. Cheng S.S., Lin S.S., Existence and Uniqueness Theorems for nonlinear difference boundary value problems, Utilitas Math. 39 (1991), 167-186. (1991) Zbl0729.39002MR1119771
  8. Ehme J., Henderson J., Multipoint boundary value problems for weakly coupled equations, Nonlinear Times and Digest 1 (1994), 133-140. (1994) Zbl0801.34024MR1272417
  9. Gaines R., Difference equations associated with boundary value problems for second order nonlinear ordinary differential equations, SIAM J. Numer. Anal. 11 (1974), 411-434. (1974) Zbl0279.65068MR0383757
  10. Henderson J., Thompson H.B., Difference equations associated with boundary value problems for second order nonlinear ordinary differential equations, to appear in J. Differ. Equations Appl. MR1923625
  11. Kelley W.G., Peterson A.C., Difference Equations, Academic Press, Boston, 1991. Zbl0970.39001MR1142573
  12. Bernfeld S.R., Lakshmikantham V., An Introduction to Nonlinear Boundary Value Problems, Academic Press, New York, 1974. MR0445048
  13. Lakshmikantham V., Trigiante D., Theory of Difference Equations: Numerical Methods and Applications, Academic Press, Boston, 1988. Zbl1014.39001MR0939611
  14. Thompson H.B., Second order differential equations with fully nonlinear two point boundary value problems, Pacific J. Math. 172 (1996), 255-277. (1996) MR1379297
  15. Thompson H.B., Tisdell C.C., Nonlinear multipoint boundary value problems for weakly coupled systems, Bull. Austral. Math. Soc. 60 (1999), 45-54. (1999) Zbl0940.34011MR1702842
  16. Thompson H.B., Tisdell C., Systems of difference equations associated with boundary value problems for second order systems of ordinary differential equations, J. Math. Anal. Appl. 248 (2000), 333-347. (2000) Zbl0963.65081MR1775855
  17. Wan Zhuang, Yubo Chen, Monotone Methods for a discrete boundary problem, Comput. Math. Appl. 32 (1996), 41-49. (1996) MR1434605

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