Abstract

We study positive solutions of an equation with singular nonlinearities. The equation arises in the study of equilibrium states of thin films. Under weak assumptions on the nonlinearity, we show that for N ≥ 3 there exists a family of radial solutions {u_α}_α>0 with u_α(0) = α and each of them is oscillatory in (0,∞). We obtain then a singular radial solution in (0,∞) by taking the limit α → 0. Meanwhile, using the solutions obtained in (0,∞), we show some existence results for the corresponding Neumann eigenvalue problem on a ball.

Keywords

elliptic equation with singular nonlinearity, rupture solutions, oscillation

Mathematical Subject Classification

Primary: 35J60, 35B45, 35B05

Authors