Sobolev regularity solutions for a class of singular quasilinear ODEs

Abstract

This paper considers an initial-boundary value problem for a class of singular quasilinear second-order ordinary differential equations with the constraint condition stemming from fluid mechanics. We prove that the existence of positive Sobolev regular solutions for this kind of singular quasilinear ODEs by means of a suitable Nash-Moser iteration scheme Meanwhile, asymptotic expansion of those positive solutions is shown.

Keywords

• sobolev regularity solution
• quasi-linear ode
• 35j25
• 35b65