Point Rupture Solutions of Singular Elliptic Equations in N-D

Abstract

We consider the elliptic equationwhere f is a positive continuous function satisfyingMotivated by the thin film equations, a solution u is said to be a point rupture solution if for some p ∈ Ω, u (p) = 0 and u (p) > 0 in Ω\ {p}. Solving the associated ordinary differential equations confirm our main results of sufficient conditions on f for the existence uniquness of radial point rupture solution and its asymptotic behavior. Furthermore, we can prove that our results can be applied to the point rupture solutions for a class of quasi-linear elliptic equations of the form div (a (u) ∆u) = a (u) 2 |∇u| 2 + f (u)