Electronic Journal of Differential Equations,
Vol. 2006(2006), No. 102, pp. 1-9.

Title: Existence of positive solutions for higher order singular
       sublinear elliptic equations

Author: Imed Bachar (Faculte des sciences de Tunis, Tunisia)

Abstract: 
 We present existence result for the  polyharmonic nonlinear
 problem
 $$\displaylines{
 (-\Delta )^{pm} u=\varphi (.,u)+\psi (.,u),\quad \hbox{in }B \cr
 u>0,\quad \hbox{in }B \cr
 \lim_{|x|\to 1} \frac{(-\Delta )^{jm}u(x)}{(1-|x|)^{m-1}}=0,
 \quad 0\leq j\leq p-1,
 }$$
 in the sense of distributions.
 Here $m,p$ are  positive integers, $B$ is the unit ball in
 $\mathbb{R}^{n}(n\geq 2)$ and the nonlinearity is a sum of a singular and
 sublinear terms satisfying some appropriate conditions related to a
 polyharmonic Kato class of functions $\mathcal{J}_{m,n}^{(p)}$.

Submitted May 10, 2006. Published August 31, 2006.
Math Subject Classifications: 34B27, 35J40.
Key Words: Green function; higher-order elliptic equations;
           positive solution; Schauder fixed point theorem.