Geodesic
Bounded and $L^2$-solutions of certain third order non-linear differential equation with a square integrable forcing term
Kragujevac Journal of Mathematics, Tome 29 (2006) no. 1.

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This paper is concerned with the existence of bounded and $L^2-$solutions to equations of the form $$\stackrel{...}x+a(t)f(\dot{x})\ddot{x}+b(t)g(x)\dot{x}+c(t,x)= e(t),\leqno (*)$$ where $e(t)$ is a continuous square integrable function. We obtain sufficient conditions which guarantee that all solutions of the equation $(*)$ are bounded are in $L^{2}[0,\infty)$. 
@article{KJM_2006_29_1_a14,
     author = {Babatunde Sunday Ogundare and Joseph Ayanrionla Ayanjinmi and Olufemi Adeyinka Adesina},
     title = {Bounded and $L^2$-solutions of certain third order non-linear differential equation with a square integrable forcing term},
     journal = {Kragujevac Journal of Mathematics},
     pages = {151 - 156},
     publisher = {mathdoc},
     volume = {29},
     number = {1},
     year = {2006},
     zbl = {1143.34021},
     url = {http://geodesic.mathdoc.fr/item/KJM_2006_29_1_a14/}
}
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Babatunde Sunday Ogundare; Joseph Ayanrionla Ayanjinmi; Olufemi Adeyinka Adesina. Bounded and $L^2$-solutions of certain third order non-linear differential equation with a square integrable forcing term. Kragujevac Journal of Mathematics, Tome 29 (2006) no. 1. http://geodesic.mathdoc.fr/item/KJM_2006_29_1_a14/