Periodic families of solutions for difference equations with a first integral

Abstract

In the following paper we establish that a one-parameter family of N- periodic solutions out of the origin is guaranteed to exist when the dimension of the N- periodic solution space of the corresponding linear problem is unity. When this dimension is greater than unity we establish that one parameter families generically exist. These results are obtained by adapting the method of Hale3 to a N-periodic difference equation with a N-periodic first integral

AMS(MOS)::

• 39
• 34

Keywords:

• alternative method
• determining equations
• first integral
• periodic solutions
• periodic difference equations

¹The results presented here are part of the first author's Ph.D. dissertation writtern under the direction of the second author

²The first author is now with the Department of Mathematics and Computer Science at West Georgia College, Carrollton, Georgia 30118

¹The results presented here are part of the first author's Ph.D. dissertation writtern under the direction of the second author

²The first author is now with the Department of Mathematics and Computer Science at West Georgia College, Carrollton, Georgia 30118

Notes

¹The results presented here are part of the first author's Ph.D. dissertation writtern under the direction of the second author

²The first author is now with the Department of Mathematics and Computer Science at West Georgia College, Carrollton, Georgia 30118