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.