Existence of positive solutions for higher order singular sublinear elliptic equations
Electronic journal of differential equations, Tome 2006 (2006)
We present existence result for the polyharmonic nonlinear problem
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 $\mathcal{J}_{m,n}^{(p)}$.
| $\displaylines{ (-\Delta )^{pm} u=\varphi (.,u)+\psi (.,u),\quad \hbox{in }B \cr u greater than 0,\quad \hbox{in }B \cr \lim_{|x|\to 1} \frac{(-\Delta )^{jm}u(x)}{(1-|x|)^{m-1}}=0, \quad 0\leq j\leq p-1, }$ |
Classification :
34B27, 35J40
Keywords: Green function, higher-order elliptic equations, positive solution, Schauder fixed point theorem
Keywords: Green function, higher-order elliptic equations, positive solution, Schauder fixed point theorem
Bachar, Imed. Existence of positive solutions for higher order singular sublinear elliptic equations. Electronic journal of differential equations, Tome 2006 (2006). http://geodesic.mathdoc.fr/item/EJDE_2006__2006__a140/
@article{EJDE_2006__2006__a140,
author = {Bachar, Imed},
title = {Existence of positive solutions for higher order singular sublinear elliptic equations},
journal = {Electronic journal of differential equations},
year = {2006},
volume = {2006},
zbl = {1128.35322},
language = {en},
url = {http://geodesic.mathdoc.fr/item/EJDE_2006__2006__a140/}
}