Geodesic
On asymptotic behaviour of oscillatory solutions for fourth order differential equations
Electronic Journal of Differential Equations, Tome 2007 (2007).

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

Summary: We establish sufficient conditions for the linear differential equations of fourth order $$ (r(t)y'''(t))' =a(t)y(t)+b(t)y'(t)+c(t)y''(t)+f(t) $$ so that all oscillatory solutions of the equation satisfy $$ \lim_{t\to\infty}y(t)=\lim_{t\to\infty}y'(t)=\lim_{t\to\infty}y''(t)= \lim_{t\to\infty}r(t)y'''(t)=0, $$ where $r:[0,\infty)\to(0,\infty),a,b,c$ and $f:[0,\infty)\to R$ are continuous functions. A suitable Green's function and its estimates are used in this paper.
Classification : 34C10
Keywords: oscillatory solution, asymptotic behaviour 
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     author = {Padhi, Seshadev and Qian, Chuanxi},
     title = {On asymptotic behaviour of oscillatory solutions for fourth order differential equations},
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     year = {2007},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2007__2007__a74/}
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Padhi, Seshadev; Qian, Chuanxi. On asymptotic behaviour of oscillatory solutions for fourth order differential equations. Electronic Journal of Differential Equations, Tome 2007 (2007). http://geodesic.mathdoc.fr/item/EJDE_2007__2007__a74/