Oscillation of second-order nonlinear differential equations with a damping term
This paper concerns the oscillation of solutions to the differential equation $$ (r(t) x'(t))'+ p(t) x'(t) + q(t) g( x(t) ) =0, $$ where $xg(x)$ greater than 0 for all $x eq 0$, $r(t)$ greater than 0 for $tgeq t_{0}$ greater than 0. No sign conditions are imposed on $p(t)$ and $q(t)...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Texas State University
2005-07-01
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| Series: | Electronic Journal of Differential Equations |
| Subjects: | |
| Online Access: | http://ejde.math.txstate.edu/Volumes/2005/76/abstr.html |
| Summary: | This paper concerns the oscillation of solutions to the differential equation $$ (r(t) x'(t))'+ p(t) x'(t) + q(t) g( x(t) ) =0, $$ where $xg(x)$ greater than 0 for all $x eq 0$, $r(t)$ greater than 0 for $tgeq t_{0}$ greater than 0. No sign conditions are imposed on $p(t)$ and $q(t)$. Our results solve the open problem posed by Rogovchenko [27], complement the results in Sun [29], and improve a number of existing oscillation criteria. Our main results are illustrated with examples. |
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| ISSN: | 1072-6691 |