Geodesic
Boundedness of solutions to fourth-order differential equation with oscillatory restoring and forcing terms
Electronic journal of differential equations, Tome 2007 (2007)
This paper concerns the fourth order differential equation

$ x''''+ax'''+f(x'')+g(x')+h(x)=p(t). $

Using the Cauchy formula for the particular solution of non-homogeneous linear differential equations with constant coefficients, we prove that the solution and its derivatives up to order three are bounded.
Classification : 34C10, 34C11
Keywords: fourth order differential equation, bounded solution, oscillatory solution, restoring and forcing terms 
@article{EJDE_2007__2007__a149,
     author = {Omeike,  Mathew O.},
     title = {Boundedness of solutions to fourth-order differential equation with oscillatory restoring and forcing terms},
     journal = {Electronic journal of differential equations},
     year = {2007},
     volume = {2007},
     zbl = {1141.34320},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2007__2007__a149/}
}
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%A Omeike,  Mathew O.
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%J Electronic journal of differential equations
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Omeike,  Mathew O. Boundedness of solutions to fourth-order differential equation with oscillatory restoring and forcing terms. Electronic journal of differential equations, Tome 2007 (2007). http://geodesic.mathdoc.fr/item/EJDE_2007__2007__a149/