Abstract
We establish some necessary and sufficient conditions for oscillation of the solutions of the following two-dimensional difference system: , , where and are strongly superlinear or sublinear functions.
Highlights
We consider the following two-dimensional nonlinear difference system as follows: Δxn f n, yn, 1.1Δyn −g n, xn, where Δxn xn 1 − xn, Δyn yn 1 − yn, f n, u and g n, u are strongly superlinear or sublinear functions. we pose some conditions on functions f and g: H1 : uf n, u > 0 and ug n, u > 0 for u / 0; H2 : f n, u and g n, u are continuous real-valued functions, and nondecreasing with respect to u;2 H3 : it is Journal of Inequalities and Applications ∞ f n, ±c ±∞1.2 n n0 for each c > 0.Definition 1.1
1 f and g are said to be strongly superlinear if there exist constants α > 0 and β > 0 with αβ > 1, such that f n, u /|u|α sgn u and g n, u /|u|β sgn u are nondecreasing with respect to |u| for each fixed n ∈ N
2 f and g are said to be strongly sublinear if there exist constants α > 0 and β > 0 with αβ < 1, such that f n, u /|u|α sgn u and g n, u /|u|β sgn u are nonincreasing with respect to |u| for each fixed n ∈ N
Summary
We consider the following two-dimensional nonlinear difference system as follows: Δxn f n, yn , 1.1. We pose some conditions on functions f and g: H1 : uf n, u > 0 and ug n, u > 0 for u / 0; H2 : f n, u and g n, u are continuous real-valued functions, and nondecreasing with respect to u;
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
