Weak Heteroclinic Solutions and Competition Phenomena to Anisotropic Difference Equations with Variable Exponents

where ∆u(k) = u(k+1)−u(k) is the forward difference operator, Z∗ := {k ∈ Z : k 6= 0} and a, α, δ, f, g are functions to be defined later. Difference equations can be seen as a discrete counterpart of PDEs and are usually studied in connection with numerical analysis. In this way, the main operator in Problem (1.1) −∆(a(k − 1,∆u(k − 1))) can be seen as a discrete counterpart of the anisotropic operator