Geodesic
Existence of positive solutions for higher order singular sublinear elliptic equations
Electronic Journal of Differential Equations, Tome 2006 (2006).

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: 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__a140,
     author = {Bachar, Imed},
     title = {Existence of positive solutions for higher order singular sublinear elliptic equations},
     journal = {Electronic Journal of Differential Equations},
     publisher = {mathdoc},
     volume = {2006},
     year = {2006},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2006__2006__a140/}
}
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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__a140/