Oscillation for equations with positive and negative coefficients and with distributed delay I: General results
| dc.contributor.author | Berezansky, Leonid | |
| dc.contributor.author | Braverman, Elena | |
| dc.date.accessioned | 2020-09-14T16:50:19Z | |
| dc.date.available | 2020-09-14T16:50:19Z | |
| dc.date.issued | 2003-02-11 | |
| dc.description.abstract | We study a scalar delay differential equation with a bounded distributed delay, ẋ(t) + ∫th(t) x(s) dsR(t, s) - ∫tg(t) x(s) d<sub>s</sub> T (t, s) = 0, where R(t, s), T(t, s) are nonnegative nondecreasing in s for any t, R(t, h(t)) = T(t, g(t)) = 0, R(t, s) ≥ T(t, s). We establish a connection between non-oscillation of this differential equation and the corresponding differential inequalities, and between positiveness of the fundamental function and the existence of a nonnegative solution for a nonlinear integral inequality that constructed explicitly. We also present comparison theorems, and explicit non-oscillation and oscillation results. In a separate publication (part II), we will consider applications of this theory to differential equations with several concentrated delays, integrodifferential, and mixed equations. | |
| dc.description.department | Mathematics | |
| dc.format | Text | |
| dc.format.extent | 21 pages | |
| dc.format.medium | 1 file (.pdf) | |
| dc.identifier.citation | Berezansky, L., & Braverman, E. (2003). Oscillation for equations with positive and negative coefficients and with distributed delay I: General results. <i>Electronic Journal of Differential Equations, 2003</i>(12), pp. 1-21. | |
| dc.identifier.issn | 1072-6691 | |
| dc.identifier.uri | https://hdl.handle.net/10877/12603 | |
| dc.language.iso | en | |
| dc.publisher | Southwest Texas State University, Department of Mathematics | |
| dc.rights | Attribution 4.0 International | |
| dc.rights.uri | https://creativecommons.org/licenses/by/4.0/ | |
| dc.source | Electronic Journal of Differential Equations, 2003, San Marcos, Texas: Southwest Texas State University and University of North Texas. | |
| dc.subject | Oscillation | |
| dc.subject | Non-oscillation | |
| dc.subject | Distributed delay | |
| dc.subject | Comparison theorems | |
| dc.title | Oscillation for equations with positive and negative coefficients and with distributed delay I: General results | |
| dc.type | Article |