Geodesic
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

$\displaylines{ (-\Delta )^{pm} u=\varphi (.,u)+\psi (.,u),\quad \hbox{in }B \cr u greater than 0,\quad \hbox{in }B \cr \lim_{|x|\to 1} \frac{(-\Delta )^{jm}u(x)}{(1-|x|)^{m-1}}=0, \quad 0\leq j\leq p-1, }$

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 $\mathcal{J}_{m,n}^{(p)}$.
Classification : 34B27, 35J40
Keywords: Green function, higher-order elliptic equations, positive solution, Schauder fixed point theorem 
@article{EJDE_2006__2006__a40,
     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__a40/}
}
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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__a40/