In this paper, we deal with the existence of a non-trivial solution for the following fractional discrete boundary-value problem for any k 2 [1; T ]N0 { T +1∇α k (k ∇α 0 (u(k))) + k ∇α 0 (T +1∇α k (u(k))) + ϕp(u(k)) = f (k; u(k)); u(0) = u(T + 1) = 0; where 0 < < 1 and k ∇α 0 is the left nabla discrete fractional difference and T +1∇α k is the right nabla discrete fractional difference f : [1; T ]N0 R ! R is a continuous function, > 0 is a parameter and ϕp is the so called p-Laplacian operator defined as ϕp(s) = jsjp−2s and 1 < p < +1. The technical method is variational approach for differentiable functionals. Several examples are included to illustrate the main results.
Khaleghi MoghadammohsenKhaleghi Moghadam,M. (2023). A survey on existence of a solution to fractional difference boundary value problem with $|u|^{p-2}u$ term. Mathematical Analysis and Convex Optimization, 4(1), 45-59. doi: 10.22034/maco.4.1.4
MLA
Khaleghi MoghadammohsenKhaleghi Moghadam,M. . "A survey on existence of a solution to fractional difference boundary value problem with $|u|^{p-2}u$ term", Mathematical Analysis and Convex Optimization, 4, 1, 2023, 45-59. doi: 10.22034/maco.4.1.4
HARVARD
Khaleghi MoghadammohsenKhaleghi Moghadam M. (2023). 'A survey on existence of a solution to fractional difference boundary value problem with $|u|^{p-2}u$ term', Mathematical Analysis and Convex Optimization, 4(1), pp. 45-59. doi: 10.22034/maco.4.1.4
CHICAGO
M. Khaleghi MoghadammohsenKhaleghi Moghadam, "A survey on existence of a solution to fractional difference boundary value problem with $|u|^{p-2}u$ term," Mathematical Analysis and Convex Optimization, 4 1 (2023): 45-59, doi: 10.22034/maco.4.1.4
VANCOUVER
Khaleghi MoghadammohsenKhaleghi Moghadam M. A survey on existence of a solution to fractional difference boundary value problem with $|u|^{p-2}u$ term. MACO, 2023; 4(1): 45-59. doi: 10.22034/maco.4.1.4
Mathematical Analysis and Convex Optimization