Asymptotic representations of solutions of nonlinear two term difference equations

作者：Kharkov V^*; Berdnikov A^*

来源：Journal of Difference Equations and Applications, 2018, 24(7): 1031-1043.

DOI：10.1080/10236198.2018.1449838

• Emden-Fowler difference equation
• regularly varying function
• asymptotic representation
• quasi-linear system

In this paper we establish the necessary and sufficient conditions for existence of P(.) solutions of the nonlinear two term difference equation Delta 2yn = pn.(yn+ s0).(Delta yn+ s1) sgn(yn+ s0), where. and. are regularly varying functions, s0, s1. Z. Also we obtain their asymptotic representations as n. +8. Since. and. could be more complicated than power functions and s0, s1. Z, for proving the main result we formulate and prove an additional statement about existence of vanishing solutions of quasilinear system of difference equations.

• 出版日期2018