Electron. J. Diff. Equ., Vol. 2010(2010), No. 15, pp. 1-10.

Entire solutions for a class of p-Laplace equations in R^2

Zheng Zhou

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.

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Zheng Zhou
College of Mathematics and Econometrics
Hunan University, Changsha, China
email: zzzzhhhoou@yahoo.com.cn

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