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Asymptotic Behavior of a Class of Nonlinear Differential Equations of nth Order

1988
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Proceedings of the American Mathematical Society
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In this paper we obtain a result of the asymptotic behavior of the nth order equation r¿ ("' + f(t,u,u',... ,«("-1)) = 0 under some assumptions. For n = 2 and f{t,u,u') = f{t,u), it revises the result given by Jingcheng Tong, which is not true in general. Much work has been done on the asymptotic behavior of the second order equation (1) u" + fit,u)=0. Some results of it are based on the integral inequalities of Gronwall-Bihari type. Here we quote the Theorem B in [1] as a proposition,

doi:10.2307/2046862
fatcat:ar4tietszvfkpeq7bbimtffuxm