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.

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