this paper is concerned with the following elliptic system:$$ left{ begin{array}{ll} -triangle u + b(x)nabla u + v(x)u=g(x, v), -triangle v - b(x)nabla v + v(x)v=f(x, u), end{array} right. $$ for $x in {r}^{n}$, where $v $, $b$ and $w$ are 1-periodic in $x$, and $f(x,t)$, $g(x,t)$ are super-quadratic. in this paper, we give a new technique to show the boundedness of cerami sequences and establi...

Macro-elements of smoothness C r on Powell-Sabin triangle splits are constructed for all r 0. These new elements are improvements on elements constructed in 10] in that certain unneeded degrees of freedom have been removed. A bivariate macro-element deened on a triangle T consists of a nite dimensional linear space S deened on T, and a set of linear functionals forming a basis for the dual of S...