Periodic solutions of difference equations

Dannan, Fozi M.; Elaydi, Saber; Liu, P.

doi:10.1080/10236190008808222

Cited by 36 publications

(14 citation statements)

References 13 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…That survey covers both ordinary difference equations, such as x(n + 1) = A(n)x(n), and Volterra difference equations. Although several papers [6,[8][9][10] relate to periodic solutions of systems of explicit difference equations, little work has been done on questions of the periodic solution of implicit Volterra summation equations, to the best of our knowledge.…”

Section: X(t) = F(t) +mentioning

confidence: 99%

See 1 more Smart Citation

Periodic solutions of discrete Volterra equations

Baker

Song²

2004

Mathematics and Computers in Simulation

View full text Add to dashboard Cite

In this paper, we investigate periodic solutions of linear and nonlinear discrete Volterra equations of convolution or non-convolution type with unbounded memory.For linear discrete Volterra equations of convolution type, we establish Fredholm's alternative theorem and for equations of non-convolution type, and we prove that a unique periodic solution exists for a particular bounded initial function under appropriate conditions. Further, this unique periodic solution attracts all other solutions with bounded initial function. All solutions of linear discrete Volterra equations with bounded initial functions are asymptotically periodic under certain conditions. A condition for periodic solutions in the nonlinear case is established.

show abstract

Section: X(t) = F(t) +mentioning

confidence: 99%

“…In [10], Elaydi et al gave an overview of results, that have been obtained in the last two decades, on the existence of periodic solutions of difference equations. That survey covers both ordinary difference equations, such as x(n + 1) = A(n)x(n), and Volterra difference equations.…”

Section: X(t) = F(t) +mentioning

confidence: 99%

Periodic solutions of discrete Volterra equations

Baker

Song²

2004

Mathematics and Computers in Simulation

View full text Add to dashboard Cite

show abstract

“…Recently, many papers have discussed the periodic solutions of difference equations [6][7][8][9][10][11][12][13][14]. However, the periodic solutions of systems of difference equations are less studied [15'16].…”

Section: Satisfying A(t + W) = A(t) F(t + Co Z) = F(t Z)mentioning

confidence: 99%

Existence of periodic solutions of system of difference equations

Genping

Shen

2006

Appl. Math. Chin. Univ.

View full text Add to dashboard Cite

show abstract

“…One can refer to [3,4,13,18,19,21,23,25,26], etc. for recent literature on the existence and multiplicity of periodic solutions and subharmonic solutions to difference equations.…”

Section: Introductionmentioning

confidence: 99%