Electron. J. Diff. Eqns., Vol. 2006(2006), No. 102, pp. 1-9.

Existence of positive solutions for higher order singular sublinear elliptic equations

Imed Bachar

Abstract:
We present existence result for the polyharmonic nonlinear problem
$$\displaylines{
 (-\Delta )^{pm} u=\varphi (.,u)+\psi (.,u),\quad \hbox{in }B \cr
 u greater than 0,\quad \hbox{in }B \cr
 \lim_{|x|\to 1} \frac{(-\Delta )^{jm}u(x)}{(1-|x|)^{m-1}}=0,
 \quad 0\leq j\leq p-1,
 }$$
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.

Show me the PDF file (238K), TEX file, and other files for this article.

Imed Bachar
Département de mathématiques
Faculté des sciences de Tunis
campus universitaire, 2092 Tunis, Tunisia
email: Imed.Bachar@ipeit.rnu.tn

Return to the EJDE web page