Oscillations of equations caused by several deviating arguments

Linear delay or advanced differential equations with variable coefficients and several not necessarily monotone arguments are considered, and some new oscillation criteria are given. More precisely, sufficient conditions, involving $\lim\sup$ and $\lim\inf$, are obtained, which essentially improve several known criteria existing in the literature. Examples illustrating the results are also given, numerically solved in MATLAB

Oscillation properties of second-order quasilinear difference equations with unbounded delay and advanced neutral terms

summary:We obtain some new sufficient conditions for the oscillation of the solutions of the second-order quasilinear difference equations with delay and advanced neutral terms. The results established in this paper are applicable to equations whose neutral coefficients are unbounded. Thus, the results obtained here are new and complement some known results reported in the literature. Examples are also given to illustrate the applicability and strength of the obtained conditions over the known ones

Oscillatory properties of third-order semi-noncanonical nonlinear delay difference equations

summary:We study the oscillatory properties of the solutions of the third-order nonlinear semi-noncanonical delay difference equation $$D_3y(n)+f(n)y^\beta (\sigma (n))=0,$$ where $D_3 y(n)=\Delta (b(n)\Delta (a(n)(\Delta y(n))^\alpha ))$ is studied. The main idea is to transform the semi-noncanonical operator into canonical form. Then we obtain new oscillation theorems for the studied equation. Examples are provided to illustrate the importance of the main results