Comment on ‘Nonlinear eigenvalue problems’
Abstract
The asymptotic behaviour of solutions to y^{\prime} (x)=cos [\pi xy(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\lt y and x\gt 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\lt y.
 Publication:

Journal of Physics A Mathematical General
 Pub Date:
 September 2014
 DOI:
 10.1088/17518113/47/36/368001
 arXiv:
 arXiv:1407.5835
 Bibcode:
 2014JPhA...47J8001K
 Keywords:

 Mathematical Physics
 EPrint:
 6 pages