Geodesic
ON THE EXISTENCE OF SOLUTIONS WITH PRESCRIBED ASYMPTOTIC BEHAVIOUR FOR PERTURBED NONLINEAR DIFFERENTIAL EQUATIONS OF SECOND ORDER
Glasgow mathematical journal, Tome 47 (2005) no. 1, pp. 177-185

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DOI

A global existence result for solutions $u(t)$ of the differential equation $x^{\prime \prime }+f(t,x)=p(t)$, $t\geq t_0\geq 1$, that can be written as $u(t)=P(t)+o(1)$ for all large $t$, where $P^{\prime \prime}(t)=p(t)$, is established by means of the Schauder-Tikhonov theorem. It generalizes the recent work of Lipovan [On the asymptotic behaviour of the solutions to a class of second order nonlinear differential equations, Glasgow Math. J.45 (2003), 179–87] and allows for a unifying treatment of the existence problems concerning asymptotically linear and oscillatory solutions of second order nonlinear differential equations.
DOI : 10.1017/S0017089504002228
Mots-clés : 34A34, 34C10, 34E05, 47H10 
MUSTAFA, OCTAVIAN G. ON THE EXISTENCE OF SOLUTIONS WITH PRESCRIBED ASYMPTOTIC BEHAVIOUR FOR PERTURBED NONLINEAR DIFFERENTIAL EQUATIONS OF SECOND ORDER. Glasgow mathematical journal, Tome 47 (2005) no. 1, pp. 177-185. doi: 10.1017/S0017089504002228
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     journal = {Glasgow mathematical journal},
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     year = {2005},
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