%0 Journal Article
%T Existence of positive solutions for some polyharmonic nonlinear boundary-value problems
%A Habib Maagli
%A Faten Toumi
%A Malek Zribi
%J Electronic Journal of Differential Equations
%D 2003
%I Texas State University
%X We present existence results for the polyharmonic nonlinear elliptic boundary-value problem $$displaylines{ (-Delta )^m u=f(cdot,u) quad hbox{in }B cr (frac{partial }{partial u })^j u=0quad hbox{on }partial B, quad 0leq jleq m-1. }$$ (in the sense of distributions), where $B$ is the unit ball in $mathbb{R}^n$ and $ngeq 2$. The nonlinearity $f(x,t)$ satisfies appropriate conditions related to a Kato class of functions $K_{m,n}$. Our approach is based on estimates for the polyharmonic Green function with zero Dirichlet boundary conditions and on the Schauder fixed point theorem.
%K Green function
%K positive solution
%K Schauder fixed point theorem
%K singular polyharmonic elliptic equation.
%U http://ejde.math.txstate.edu/Volumes/2003/58/abstr.html