Advances in Difference Equations (Jan 2009)

On Boundedness of Solutions of the Difference Equation <inline-formula><graphic file="1687-1847-2009-463169-i1.gif"/></inline-formula> for <inline-formula><graphic file="1687-1847-2009-463169-i2.gif"/></inline-formula>

  • Xi Hongjian,
  • Sun Taixiang,
  • Yu Weiyong,
  • Zhao Jinfeng

Journal volume & issue
Vol. 2009, no. 1
p. 463169

Abstract

Read online

We study the boundedness of the difference equation , where and the initial values . We show that the solution of this equation converges to if or for all ; otherwise is unbounded. Besides, we obtain the set of all initial values such that the positive solutions of this equation are bounded, which answers the open problem 6.10.12 proposed by Kulenović and Ladas (2002).