Some existence results for nonresonant difference equations on infinite intervals subject to nonlocal boundary conditions
DOI:
https://doi.org/10.12775/TMNA.2024.025Słowa kluczowe
Multipoint boundary value problems, nonlocal boundary conditions, $\ell^p$-space, infinite time intervals, Schauder's fixed point theoremAbstrakt
In this work we provide conditions for the existence of solutions to nonlinear boundary value problems of the form \begin{equation*} x_{k+1}=A_kx_k+f(k,x_k), \quad k\in\N_0:=\{0,1,\dots\}, \end{equation*} subject to boundary conditions \begin{equation*} \sum_{k=0}^\infty B_kx_k=G(x). \end{equation*} We will show that under appropriate assumptions on each $A_k$, $f$, each $B_k$, and $G$, $\ellp{n}$ solutions will exist for $p\in [1,\infty]$.Bibliografia
R.P. Agarwal, Difference Equations and Inequalities, Theory, Methods and Applications, Marcel Dekker, New York-Basel, 2000.
R.P. Agarwal and D. O’Regan, Boundary value problems for discrete equations, Appl. Math. Lett. 10 (1997), no. 4, 83–89.
R.P. Agarwal and D. O’Regan, Nonlinear Urysohn discrete equations on the infinite interval: a fixed-point approach, Comput. Math. Appl. 42 (2001), 273–281.
C. Bereanu, P. Jeblean and C. Serban, Periodic and Neumann problems for discrete p-Laplacian, J. Math. Anal. Appl. 399 (2013), no. 1, 75–87.
C. Bereanu and J. Mawhin, Existence and multiplicity results for periodic solutions of nonlinear difference equations, J. Difference Equ. Appl. 12 (2006), no. 7, 677–695.
G. Bonanno and P. Candito, Infinitely many solutions for a class of discrete nonlinear boundary value problems, Appl. Anal. 88 (2009), no. 4, 605–616.
G. D’Agui, J. Mawhin and A. Sciammetta, Positive solutions for a discrete two-point nonlinear boundary value problem with p-Laplacian, J. Math. Anal. Appl. 447 (2017), no. 1, 383–397.
S. Elaydi, An Introduction to Difference Equations, Springer, 2005.
B. Freedman and J. Rodrı́guez, On nonlinear boundary value problems in the discrete setting, J. Difference Equ. Appl. 25 (2019), no. 7, 994–1006.
J. Henderson, and R. Luca, Existence of positive solutions for a system of second-order multi-point discrete boundary value problems, J. Difference Equ. Appl. 19 (2013), no. 11, 1889–1906.
W.G. Kelley and A.C. Peterson, Difference Equations, Academic Press, New York, 1978.
D. Maroncelli and J. Rodrı́guez, Periodic behaviour of nonlinear, second-order discrete dynamical systems, J. Difference Equ. Appl. 22 (2016), no. 2, 280–294.
J. Rodrı́guez, Nonlinear discrete systems with global boundary conditions, J. Math. Anal. Appl. 286 (2003), no. 2, 782–794.
J. Rodrı́guez and D. Sweet, Discrete boundary value problems on infinite intervals, J. Difference Equ. Appl. 7 (2001), no. 3, 435–443.
R. Steglinski, Convex sets and n-order difference systems with nonlocal nonlinear boundary conditions, J. Difference Equ. Appl. (2018), 1065–1073.
Pobrania
Opublikowane
Jak cytować
Numer
Dział
Licencja
Prawa autorskie (c) 2025 Daniel Maroncelli, Jesús Rodríguez
Utwór dostępny jest na licencji Creative Commons Uznanie autorstwa – Bez utworów zależnych 4.0 Międzynarodowe.
Statystyki
Liczba wyświetleń i pobrań: 0
Liczba cytowań: 0
