Abstract
This paper mainly studies oscillatory of all solutions for a class higher order linear functional equations of the form
 
  x(g(t))=P(t)x(t)+∑^m_i=1 Q_i(t)x(g^(k+1)(t))
 
 Where P, Q, g:[t_0,∞]  → R^+ =[0,∞] are given real valued functions and g(t) ≠t, lim_(t→∞) g(t)=∞.
 
 Some sufficient conditions are obtained. Our results generalize or improve some results in some literature given. An example is also given to illustrate the results.
Highlights
Consider the high order functional equation : m (1.1) I, gm that m times iteration of function g means: g0(t) t, gi 1(t) g gi (t),t I,i 1,2.....m.As a solution of equation (1.1) if x : I R, such that: is setting up, satisfied (1.1) for t I ., we call this solution is oscillatory
This paper mainly studies oscillatory of all solutions for a class higher order linear functional equations of the form m x(g(t)) P(t)x(t) Qi (t)x(g k i (t)) i 1
In 1994, Golda and Werbowski firstly did the research of the oscillation of the solutions of equation (1.2), and we could know it from their research
Summary
This paper mainly studies oscillatory of all solutions for a class higher order linear functional equations of the form m x(g(t)) P(t)x(t) Qi (t)x(g k i (t)) i 1 Where P,Q,g:[t0, ] R [0, ]are given real valued functions and g An example is given to illustrate the results. Introduction Consider the high order functional equation : m x(g(t)) P(t)x(t) Qi (t)x(g k i (t)) i 1 (1.1) As a solution of equation (1.1) if x : I R , such that: sup{| x(s) |: s It0 [t0, ) I} 0 for t0 (0, )
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