Stimulated by the articles [22, 23], in this article, we should consider corresponding neutral-type difference version of (1.1) as follows: u i ( n + 1 ) = a i ( n ) u i ( n ) + ∑ j = 1 m c i j Δ u j ( n - τ ) + ∑ j = 1 m b i j ( n ) g j ( u j ( n ) ) + ∑ j = 1 m d i j ( n ) g j ∑ v = 1 ∞ h j ( v ) u j ( n - v ) + I i ( n ), (1.2).
Finally, under our weaker assumption on f (see (H1) and (H2) for details), since we cannot verify that the corresponding functional for the associated problem satisfies the P.S. condition, we consider the corresponding truncated problem.
Furthermore, we consider the corresponding homogeneous linear equation.
via the Hadamard product given by (1.3), we consider a corresponding function (1.7).
In this article, we consider the corresponding problems in higher dimensional setting.
Given a quasi-ordered set ( X, ⪯ ), we consider the corresponding quasi-ordered set ( X m, ≼ I ).
Along with system (3) we consider the corresponding vector map F = ( f, x n, g, y n ).
In this paper, we consider the corresponding stochastic problem of a deterministic system by introducing noises in system (2).
By referring to [14, 18] and observing Figures 1-4, we consider the corresponding Gauss theorem in four dimensions for the components of f in (mathbb{S}).
We consider the corresponding crossed product C⁎-algebra for discrete countable groups that are central extensions of finitely generated abelian groups by finitely generated abelian groups (these are automatically residually finite).
