Geodesic
Boundedness of solutions to fourth-order differential equation with oscillatory restoring and forcing terms
Electronic Journal of Differential Equations, Tome 2007 (2007).

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

Summary: 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 
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     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},
     publisher = {mathdoc},
     volume = {2007},
     year = {2007},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2007__2007__a249/}
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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__a249/