Some existence results for nonresonant difference equations on infinite intervals subject to nonlocal boundary conditions
DOI:
https://doi.org/10.12775/TMNA.2024.025Keywords
Multipoint boundary value problems, nonlocal boundary conditions, $\ell^p$-space, infinite time intervals, Schauder's fixed point theoremAbstract
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 $p\in [1,\infty]$.References
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