Stavroulakis, Ioannis P.

Oscillation criteria for functional differential equations

Electron. J. Differ. Equ. 2005, 171-180, electronic only (2005)

Summary

Summary: Consider the first-order linear delay differential equation $$ x'(t)+p(t)x(\tau (t))=0,\quad t\geq t_{0}, $$ and the second-order linear delay equation $$ x''(t)+p(t)x(\tau (t))=0,\quad t\geq t_{0}, $$ where $$ 0<\liminf_{t\to \infty }\int_{\tau (t)}^{t}p(s)ds\leq \frac{1}{e} \quad \hbox{and}\quad \limsup_{t\to \infty }\int_{\tau (t)}^{t}p(s)ds<1, $$ and for the second-order equation when $$ \liminf_{t\to \infty }\int_{\tau (t)}^{t}\tau (s)p(s)ds \leq \frac{1}{e}\quad \hbox{and}\quad \limsup_{t\to \infty }\int_{\tau (t)}^{t}\tau (s)p(s)ds<1\,. $$

Mathematics Subject Classification

34K11, 34C10

Keywords/Phrases

oscillation, delay differential equations

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