Proceedings of the Royal Society of Edinburgh: Section A Mathematics

Table of Contents - 1978 - Volume 81, Issue 3-4  

Research Article

Oscillatory and asymptotic behaviour of all solutions of differential equations with deviating arguments†

Ch. G. Philosa1

a1 Department of Mathematics, University of Ioannina, Greece

Synopsis

This paper deals with the oscillatory and asymptotic behaviour of all solutions of a class of nth order (n > 1) non-linear differential equations with deviating arguments involving the so called nth order r-derivative S0308210500010556_inline1 of the unknown function x defined by

S0308210500010556_eqnU1

where r1, (i = 0,1,…, n – 1) are positive continuous functions on [t0, ∞). The results obtained extend and improve previous ones in [7 and 15] even in the usual case where r0 = r1 = … = rn–1 = 1.

(Received May 18 1977)

Footnotes

† This paper formed a part of the author's Doctoral Thesis submitted to the School of Physics and Mathematics, University of Ioannina.