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Comment on 'Nonlinear eigenvalue problems'

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

Abstract

The asymptotic behaviour of solutions to y'(x)=cos[πxy(x)] was investigated by Bender et al (2014 J. Phys. A: Math. Theor. 47 235204). 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
Additional Information: This is an author-created, un-copyedited version of an article accepted for publication/published in Journal of Physics A: Mathematical and Theoretical. IOP Publishing Ltd is not responsible for any errors or omissions in this version of the manuscript or any version derived from it. The Version of Record is available online at https://doi.org/10.1088/1751-8113/47/36/368001.
Subjects: Q Science > QA Mathematics
Departments: School of Mathematics, Computer Science & Engineering
URI: http://openaccess.city.ac.uk/id/eprint/17470
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