Multipoint boundary value problems for discrete equations
Drábek, Pavel ; Thompson, Harold Bevan ; Tisdell, Christopher
Commentationes Mathematicae Universitatis Carolinae, Tome 42 (2001), p. 459-468 / Harvested from Czech Digital Mathematics Library
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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.

Publié le : 2001-01-01
Classification:  34B10,  39A10,  39A12 
@article{119260,
     author = {Pavel Dr\'abek and Harold Bevan Thompson and Christopher Tisdell},
     title = {Multipoint boundary value problems for discrete equations},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     volume = {42},
     year = {2001},
     pages = {459-468},
     zbl = {1055.39027},
     mrnumber = {1859593},
     language = {en},
     url = {http://dml.mathdoc.fr/item/119260}
}

Drábek, Pavel; Thompson, Harold Bevan; Tisdell, Christopher. Multipoint boundary value problems for discrete equations. Commentationes Mathematicae Universitatis Carolinae, Tome 42 (2001) pp. 459-468. http://gdmltest.u-ga.fr/item/119260/

Agarwal R.P. On multipoint boundary value problems for discrete equations, J. Math. Anal. Appl. 96 (1983), 520-534. (1983) | MR 0719333 | Zbl 0539.39005

Agarwal R.P. On boundary value problems for second order discrete systems, Appl. Anal. 20 (1985), 1-17. (1985) | MR 0808054 | Zbl 0596.39003

Agarwal R.P. Difference Equations and Inequalities, Marcel Dekker, New York, 1992. | MR 1155840 | Zbl 0952.39001

Agarwal R.P.; O'Regan D. Boundary value problems for discrete equations, Appl. Math. Lett. 10 (1997), 83-89. (1997) | MR 1458158 | Zbl 0890.39001

Agarwal R.P.; O'Regan D. Difference equations in abstract spaces, J. Austral. Math. Soc. (Series A) 64 (1998 277-284). (1998 277-284) | MR 1619810

Agarwal R.P.; O'Regan D. Singular discrete boundary value problems, Appl. Math. Lett. 12 (1999), 127-131. (1999) | MR 1750610 | Zbl 0944.39003

Cheng S.S.; Lin S.S. Existence and Uniqueness Theorems for nonlinear difference boundary value problems, Utilitas Math. 39 (1991), 167-186. (1991) | MR 1119771 | Zbl 0729.39002

Ehme J.; Henderson J. Multipoint boundary value problems for weakly coupled equations, Nonlinear Times and Digest 1 (1994), 133-140. (1994) | MR 1272417 | Zbl 0801.34024

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) | MR 0383757 | Zbl 0279.65068

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. | MR 1923625

Kelley W.G.; Peterson A.C. Difference Equations, Academic Press, Boston, 1991. | MR 1142573 | Zbl 0970.39001

Bernfeld S.R.; Lakshmikantham V. An Introduction to Nonlinear Boundary Value Problems, Academic Press, New York, 1974. | MR 0445048

Lakshmikantham V.; Trigiante D. Theory of Difference Equations: Numerical Methods and Applications, Academic Press, Boston, 1988. | MR 0939611 | Zbl 1014.39001

Thompson H.B. Second order differential equations with fully nonlinear two point boundary value problems, Pacific J. Math. 172 (1996), 255-277. (1996) | MR 1379297

Thompson H.B.; Tisdell C.C. Nonlinear multipoint boundary value problems for weakly coupled systems, Bull. Austral. Math. Soc. 60 (1999), 45-54. (1999) | MR 1702842 | Zbl 0940.34011

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) | MR 1775855 | Zbl 0963.65081

Wan Zhuang; Yubo Chen Monotone Methods for a discrete boundary problem, Comput. Math. Appl. 32 (1996), 41-49. (1996) | MR 1434605