Geodesic
Existence of solutions to higher-order discrete three-point problems
Electronic Journal of Differential Equations, Tome 2003 (2003).

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: We are concerned with the higher-order discrete three-point boundary-value problem $$\displaylines{ (\Delta^n x)(t)=f(t,x(t+\theta)), \quad t_1\le t\le t_3-1, \quad -\tau\le \theta\le 1\cr (\Delta^i x)(t_1)=0, \quad 0\le i\le n-4, \quad n\ge 4 \cr \alpha (\Delta^{n-3}x)(t)-\beta (\Delta^{n-2}x)(t)=\eta(t), \quad t_1-\tau-1\le t\le t_1 \cr (\Delta^{n-2}x)(t_2)=(\Delta^{n-1}x)(t_3)=0. }$$ By placing certain restrictions on the nonlinearity and the distance between boundary points, we prove the existence of at least one solution of the boundary value problem by applying the Krasnoselskii fixed point theorem.
Classification : 39A10
Keywords: difference equations, boundary-value problem, Green's function, fixed points, cone 
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     author = {Anderson, Douglas R.},
     title = {Existence of solutions to higher-order discrete three-point problems},
     journal = {Electronic Journal of Differential Equations},
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     volume = {2003},
     year = {2003},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2003__2003__a31/}
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Anderson, Douglas R. Existence of solutions to higher-order discrete three-point problems. Electronic Journal of Differential Equations, Tome 2003 (2003). http://geodesic.mathdoc.fr/item/EJDE_2003__2003__a31/