A Neumann problem for quasilinear elliptic equations with logarithmic nonlinearity in a ball

Abstract

The quasilinear elliptic problem −div(|∇u| ^p−2∇u) = log u ^p−1 + h(x)u ^q in a ball B _R ⊂ R ^N with Neumann boundary conditions ∂_ν u = 0 on ∂B _R were studied. By means of a double perturbation argument, we obtain a positive radial solution .

Keywords:

• singular elliptic equation
• Neumann problem
• regularity

AMS Subject Classifications::

• 35J05
• 35J62

Acknowledgements

The project Supported by the National Natural Science Foundation of China (No. 10871060); the Natural Science Foundation of Jiangsu Higher Education Institutions of China (No. 08KJB110005).