An improved oscillation criterion for first order difference equations

作者：Ocalan Ozkan^*

来源：Bulletin Mathematique de la Societe des Sciences Mathematiques de Roumanie, 2016, 59(1): 65-73.

• Delay difference equation
• general argument
• oscillation

This paper is concerned with the oscillatory behavior of first order difference equation with general argument
Delta x(n) + p(n)x (tau(n)) = 0, n = 0, 1,... (*)
where (p(n)) is a sequence of nonnegative real numbers and (tau(n)) is a sequence of integers. Let the number m be defined by
m = lim inf(n ->infinity) Sigma(j=tau(n))(n-1) p(j)(j- tau(j))+1/j- tau(j)))(j- tau(j)+1)
It is proved that, all solutions of Equation (*) oscillate if the condition
m>1
is satisfied.

• 出版日期2016