Geodesic
Existence of positive solutions for some polyharmonic nonlinear boundary-value problems
Electronic Journal of Differential Equations, Tome 2003 (2003).

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

Summary: We present existence results for the polyharmonic nonlinear elliptic boundary-value problem $$\displaylines{ (-\Delta )^m u=f(\cdot,u) \quad \hbox{in }B \cr (\frac{\partial }{\partial \nu })^j u=0\quad \hbox{on }\partial B, \quad 0\leq j\leq m-1. }$$ (in the sense of distributions), where $B$ is the unit ball in $\mathbb{R}^n$ and $n\geq 2$. The nonlinearity $f(x,t)$ satisfies appropriate conditions related to a Kato class of functions $K_{m,n}$. Our approach is based on estimates for the polyharmonic Green function with zero Dirichlet boundary conditions and on the Schauder fixed point theorem.
Classification : 34B27, 35J40
Keywords: Green function, positive solution, Schauder fixed point theorem, singular polyharmonic elliptic equation 
@article{EJDE_2003__2003__a170,
     author = {M\^aagli, Habib and Toumi, Faten and Zribi, Malek},
     title = {Existence of positive solutions for some polyharmonic nonlinear boundary-value problems},
     journal = {Electronic Journal of Differential Equations},
     publisher = {mathdoc},
     volume = {2003},
     year = {2003},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2003__2003__a170/}
}
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Mâagli, Habib; Toumi, Faten; Zribi, Malek. Existence of positive solutions for some polyharmonic nonlinear boundary-value problems. Electronic Journal of Differential Equations, Tome 2003 (2003). http://geodesic.mathdoc.fr/item/EJDE_2003__2003__a170/