City Research Online

Abstract

The asymptotic behaviour of solutions to $y'(x)=\cos[\pi x y(x)]$ was investigated by Bender, Fring and Komijani (2014). They found, for example, a relation between the initial value $y(0)=a$ and the number of maxima that the solution exhibited. We present an alternative derivation of the asymptotic results that looks at the solutions in the regions $x<y$ and $x>y$, and confirms the behaviour found previously for larger values of $a$. This method uses the small amplitude and high frequency of the oscillatory behaviour in the region $x<y$.

Publication Type:	Article
Publisher Keywords:	asymptotics, eigenvalues, ordinary differential equations
Subjects:	Q Science > QA Mathematics
Departments:	School of Science & Technology > Mathematics

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