LAYERED SOLUTIONS IN R 2 FOR A CLASS OF p-LAPLACE EQUATIONS

This paper studies the entire solutions of a class of p-Laplace equat ion - div(|del|(p-2)del u)+a(x)W'(u(x,y))=0, (x,y) is an element of R(2) (0.1) in the case p > 2. where a : R -> R(+) is a periodic, positive function and W : R -> R is an on-negative C(2) function. We look for the entire solutions of the above equation with a symptotic conditions u(x,y) -> +/- 1 as x -> +/-infinity uniformly with respect to y is an element of R. Via variational methods we find layered solutions which depend on both x and y, i.e., solutions which do not exhibit one dimensional symmetries.