Electronic Journal of Differential Equations,
Vol. 2010(2010), No. 15, pp. 1-10.
Title: Entire solutions for a class of p-Laplace equations in R^2
Author: Zheng Zhou (Hunan Univ., Changsha, China)
Abstract:
We study the entire solutions of
the p-Laplace equation
$$
-\hbox{div}(|\nabla u|^{p-2}\nabla u)+a(x,y)W'(u(x,y))=0, \quad
(x,y)\in {\mathbb{R}}^2
$$
where a(x,y) is a periodic in x and y, positive function. Here
$W:\mathbb{R}\to\mathbb{R}$ is a two well potential. Via variational
methods, we show that there is layered solution which is heteroclinic
in x and periodic in y direction.
Submitted September 15, 2009. Published January 21, 2010.
Math Subject Classifications: 35J60, 35B05, 35B40.
Key Words: Entire solution; p-Laplace Allen-Cahn equation;
Variational methods.