# Comment on "Nonlinear eigenvalue problems"

Kerr, O. (2014). Comment on "Nonlinear eigenvalue problems". Journal of Physics A: Mathematical and Theoretical, 47, p. 368001. doi: 10.1088/1751-8113/47/36/368001

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## 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 $x<y$.

Item Type: Article asymptotics, eigenvalues, ordinary differential equations Q Science > QA Mathematics School of Engineering & Mathematical Sciences > Department of Mathematical Science http://openaccess.city.ac.uk/id/eprint/3829