Oscillation analysis for nonlinear difference equation with non-monotone arguments

• Main Authors: Özkan Öcalan, Umut Mutlu Özkan, Mustafa Kemal Yildiz
• Format: Article
• Language: English
• Published: SpringerOpen 2018-05-01
• Series: Advances in Difference Equations
• Subjects: Delay difference equation; Non-monotone arguments; Nonlinear; Oscillation
• Online Access: http://link.springer.com/article/10.1186/s13662-018-1630-y

Abstract The aim of this paper is to obtain some new oscillatory conditions for all solutions of nonlinear difference equation with non-monotone or non-decreasing argument Δx(n)+p(n)f(x(τ(n)))=0,n=0,1,…, $$ \Delta x(n)+p(n)f \bigl( x \bigl( \tau (n) \bigr) \bigr) =0,\quad n=0,1,\ldots , $$where (p(n)) $( p(n) ) $ is a sequence of nonnegative real numbers and (τ(n)) $( \tau (n) ) $ is a non-monotone or non-decreasing sequence, f∈C(R,R) $f\in C(\mathbb{R},\mathbb{R})$ and xf(x)>0 $xf(x)>0$ for x≠0 $x\neq 0$.