Abstract A new method for solving the boundary value problems second order ODEs with bounded nonlinearities and singular $$\varphi $$ φ –Laplacians is presented.

Using singular spectral theory, a boundary-initial value problem is solved for the interfacial concentration of a surfactant on a liquid droplet oscillating in a surrounding second immiscible liquid phase. Besides being of value to the specific application the methodology of this paper is useful for a variety of boundary-initial value problems of interest to chemical engineers in which material...