Asymptotic distributions of Neumann problem for Sturm-Liouville equation

In this paper we apply the Homotopy perturbation method to derive the higher-order asymptotic distribution of the eigenvalues and eigenfunctions associated with the linear real second order equation of Sturm-liouville type on [۰,pi] with Neumann conditions (y'(۰)=y'(pi)=۰) where q is a real-valued Sign-indefinite number of C^{۱}[۰,pi] and lambda is a real parameter.

Keywords:

Sturm-Liouville , Nondefinite problem , Homotopy perturbation method , Asymptotic distribution