Geodesic
Necessary and sufficient conditions for the oscillation a third-order differential equation
Electronic Journal of Differential Equations, Tome 2010 (2010).

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: We show that under certain restrictions the following three conditions are equivalent: The equation $$ y'''+a(t)y''+b(t)y'+c(t)y=f(t) $$ is oscillatory. The equation $$ x'''+a(t)x''+b(t)x'+c(t)x=0 $$ is oscillatory. The second-order Riccati equation $$ z''+3zz'+a(t)z'=z^3+a(t)z^2+b(t)z+c(t) $$ does not admit a non-oscillatory solution that is eventually positive. Furthermore, we obtain sufficient conditions for the above statements to hold, in terms of the coefficients. These conditions are sharp in the sense that they are both necessary and sufficient when the coefficients $a(t), b(t), c(t)$ are constant.
Classification : 34C10, 34C15
Keywords: oscillation, non-oscillation, third order differential equations 
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     author = {Das, Pitambar and Pati, Jitendra Kumar},
     title = {Necessary and sufficient conditions for the oscillation a third-order differential equation},
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     volume = {2010},
     year = {2010},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2010__2010__a286/}
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Das, Pitambar; Pati, Jitendra Kumar. Necessary and sufficient conditions for the oscillation a third-order differential equation. Electronic Journal of Differential Equations, Tome 2010 (2010). http://geodesic.mathdoc.fr/item/EJDE_2010__2010__a286/