@ARTICLE{Khaleghi Moghadam,
author = {Khaleghi Moghadam, Mohsen and },
title = {A survey on existence of a solution to fractional difference boundary value problem with $|u|^{p-2}u$ term},
volume = {4},
number = {1},
abstract ={In this paper, we deal with the existence of a non-trivial solution for the following fractional discrete boundary-value problem for any $k in [1,T]_{mathbb{N}_{0}}$ begin{equation*} begin{cases} _{T+1}nabla_k^{alpha}left( ^{}_knabla_{0}^{alpha}(u(k))right)+{^{}_knabla}_{0}^{alpha}left( ^{}_{T+1}nabla_k^{alpha}(u(k))right)+phi_{p}(u(k))=lambda f(k,u(k)), u(0)= u(T+1)=0, end{cases} end{equation*} where $0< alpha<1$ and $^{}_knabla_{0}^{alpha}$ is the left nabla discrete fractional difference and $^{}_{T+1}nabla_k^{alpha}$ is the right nabla discrete fractional difference $f: [1,T]_{mathbb{N}_{0}}timesmathbb{R}tomathbb{R}$ is a continuous function, $lambda>0$ is a parameter and $phi _{p}$ is the so called $p$-Laplacian operator defined as $phi _{p}(s)=|s|^{p-2}s$ and $1 },
URL = {http://maco.lu.ac.ir/article-1-128-en.html},
eprint = {http://maco.lu.ac.ir/article-1-128-en.pdf},
journal = {Mathematical Analysis and Convex Optimization},
doi = {10.22034/maco.4.1.4},
year = {2023}
}