English

Oscillation criteria for differential equations with several retarded arguments

Classical Analysis and ODEs 2021-02-09 v2

Abstract

Consider the first-order linear differential equation with several retarded arguments x(t)+i=1mpi(t)x(τi(t))=0,      tt0, x^{\prime}(t)+\sum\limits_{i=1}^{m}p_{i}(t)x(\tau_{i}(t))=0,\;\;\;t\geq t_{0}, where the functions pi,τiC([t0,),R+),p_{i},\tau_{i}\in C([t_{0,}\infty),\mathbb{R}^{+}), for every i=1,2,,m,i=1,2,\ldots,m, τi(t)t\tau_{i}(t)\leq t \ for tt0t\geq t_{0} and % \lim_{t\rightarrow \infty}\tau_{i}(t)=\infty . The state of the art on the oscillation of all solutions to these equations are established especially in the case of non-monotone arguments. Examples illustrating the results are given.

Keywords

Cite

@article{arxiv.1309.6213,
  title  = {Oscillation criteria for differential equations with several retarded arguments},
  author = {Gennaro Infante and Roman Koplatadze and Ioannis P. Stavroulakis},
  journal= {arXiv preprint arXiv:1309.6213},
  year   = {2021}
}

Comments

14 pages, paper to appear in Funkcialaj Ekvacioj

R2 v1 2026-06-22T01:33:08.444Z