A survey on existence of a solution to fractional difference boundary value problem with |u|^{p-2}u term

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

کلیدواژه های A survey on existence of a solution to fractional difference boundary value problem with |u|^{p-2}u term:

Discrete fractional calculus ، Discrete nonlinear boundary value problem ، Non trivial solution ، Variational methods ، Critical point theory.