scholarly journals On asymptotic behavior of solutions to the fourth order cubic nonlinear Schrödinger type equation

2019 ◽  
Author(s):  
Jun-ichi Segata
Keyword(s):  
Asymptotic Behavior ◽  
Fourth Order ◽  
Type Equation ◽  
Asymptotic Behavior Of Solutions ◽  
Nonlinear Schrödinger

scholarly journals Asymptotic Properties of Solutions to Second-Order Difference Equations of Volterra Type

2018 ◽  
Vol 2018 ◽  
pp. 1-10 ◽  
Author(s):  
Janusz Migda ◽  
Małgorzata Migda ◽  
Magdalena Nockowska-Rosiak
Keyword(s):  
Asymptotic Behavior ◽  
Difference Equations ◽  
Existence Of Solutions ◽  
Asymptotic Properties ◽  
Sufficient Conditions ◽  
Type Equation ◽  
Asymptotic Behavior Of Solutions ◽  
Volterra Type ◽  
Order Difference ◽  
Prescribed Asymptotic Behavior

We consider the discrete Volterra type equation of the form Δ(rnΔxn)=bn+∑k=1nK(n,k)f(xk). We present sufficient conditions for the existence of solutions with prescribed asymptotic behavior. Moreover, we study the asymptotic behavior of solutions. We use o(ns), for given nonpositive real s, as a measure of approximation.

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