Bounded Solutions to Nonhomogeneous Linear Second-Order Difference Equations

Abstract

By using some solvability methods and the contraction mapping principle are investigated bounded, as well as periodic solutions to some classes of nonhomogeneous linear second-order difference equations on domains N 0 , Z \ N 2 and Z. The case when the coefficients of the equation are constant and the zeros of the characteristic polynomial associated to the corresponding homogeneous equation do not belong to the unit circle is described in detail.

Solvability and semi‐cycle analysis of a class of nonlinear systems of difference equations

“…From (54) to (56), (58) to (60), and the method of induction, it follows that (57) holds for every m ∈ N 0 . By using the changes of variables…”

“…One of the reasons why solvability of difference equations is always a popular topic lies in its enormous applicability (see, eg, previous studies [17][18][19][20]22,24,[53][54][55][56][57][58][59][60][61][62] ). Some other results in the topic can be also found in other related works.…”

More on a hyperbolic‐cotangent class of difference equations

“…For some applications of solvability and related things, see the previous studies. [15][16][17][18]20,22,[44][45][46][47][48][49][50][51][52][53] Some product-type difference equations and systems have been essentially solved by using the linear ones but in a more complex way. [54][55][56][57][58][59][60][61] Several methods, including the method of transformation and methods connected to product-type equations and systems, can be found in the representative paper.…”

Solvability of eight classes of nonlinear systems of difference equations

“…We would also like to mention that solvable difference equations have numerous applications in nature, society, and other areas of mathematics and science (see, eg, previous works [16][17][18][19]21,23,[60][61][62][63][64][65][66][67][68][69] ). For some other related results, see also other works.…”