arXiv subjects
Publications and source records attributed to Ioannis P. Stavroulakis.
Sufficient oscillation conditions involving $\limsup $ and $\liminf $ for first-order differential equations with several non-monotone deviating arguments and nonnegative coefficients are obtained. The results are based on the iterative application of the Grönwall inequality. Examples illustrating the significance of the results are also given.
We consider difference equations with several non-monotone deviating arguments and nonnegative coefficients. The deviations (delays and advances) are, generally, unbounded. Sufficient oscillation conditions are obtained in an explicit iterative form. Additional results in terms of $\liminf $ are obtained for bounded deviations. Examples illustrating the oscillation tests are presented.
Consider the first-order linear differential equation with several retarded arguments $$ x^{\prime}(t)+\sum\limits_{i=1}^{m}p_{i}(t)x(τ_{i}(t))=0,\;\;\;t\geq t_{0}, $$ where the functions $p_{i},τ_{i}\in C([t_{0,}\infty),\mathbb{R}^{+}),$ for every $i=1,2,\ldots,m,$ $τ_{i}(t)\leq t$ \ for $t\geq t_{0}$ and $% \lim_{t\rightarrow \infty}τ_{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.