Electronic Journal of Differential Equations,
Vol. 2009(2009), No. 87, pp. 1-10.

Title: Existence of solutions to p-Laplace equations with
       logarithmic nonlinearity

Authors: Jing Mo      (Nanjing Normal Univ., Jiangsu, China)
         Zuodong Yang (Nanjing Normal Univ., Jiangsu, China)

Abstract:
 This article concerns the the nonlinear elliptic equation
 $$
 -\hbox{div}(|\nabla u|^{p-2}\nabla u)
 =\log u^{p-1}+\lambda f(x,u)
 $$
 in a bounded domain $\Omega \subset \mathbb{R}^{N}$ with $N\geq 1$
 and $u=0$ on $\partial\Omega$. By  means of a double
 perturbation argument, we obtain a nonnegative solution.
 
Submitted February 23, 2009. Published July 10, 2009.
Math Subject Classifications: 35B20, 35B65, 35J65.
Key Words: Existence; logarithmic nonlinearity; supersolution; 
           subsolution.