Electron. J. Diff. Eqns., Vol. 2009(2009), No. 87, pp. 1-10.

Existence of solutions to p-Laplace equations with logarithmic nonlinearity

Jing Mo, Zuodong Yang

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.

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  Jing Mo
Institute of Mathematics, School of Mathematics Science
Nanjing Normal University
Jiangsu Nanjing 210097, China
email: jingshuihailang@163.com
Zuodong Yang
Institute of Mathematics, School of Mathematics Science
Nanjing Normal University
Jiangsu Nanjing 210097, China
email: zdyang_jin@263.net

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