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.