Geodesic
Existence of continuous positive solutions for some nonlinear polyharmonic systems outside the unit ball
Electronic journal of differential equations, Tome 2011 (2011)
We study the existence of continuous positive solutions of the m-polyharmonic nonlinear elliptic system

$\displaylines{ (-\Delta)^{m}u+\lambda p(x)g(v)=0,\cr (-\Delta )^{m}v+\mu q(x)f(u)=0 }$

in the complement of the unit closed ball in $\mathbb{R}^{n}$ (n>2m and $m\geq 1$). Here the constants $\lambda,\mu$ are nonnegative, the functions f,g are nonnegative, continuous and monotone. We prove two existence results for the above system subject to some boundary conditions, where the nonnegative functions p,q satisfy some appropriate conditions related to a Kato class of functions.
Classification : 34B27, 35J40
Keywords: polyharmonic elliptic system, positive solutions, Green function, polyharmonic Kato class 
@article{EJDE_2011__2011__a37,
     author = {Turki,  Sameh},
     title = {Existence of continuous positive solutions for some nonlinear polyharmonic systems outside the unit ball},
     journal = {Electronic journal of differential equations},
     year = {2011},
     volume = {2011},
     zbl = {1229.35063},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2011__2011__a37/}
}
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TI  - Existence of continuous positive solutions for some nonlinear polyharmonic systems outside the unit ball
JO  - Electronic journal of differential equations
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VL  - 2011
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%0 Journal Article
%A Turki,  Sameh
%T Existence of continuous positive solutions for some nonlinear polyharmonic systems outside the unit ball
%J Electronic journal of differential equations
%D 2011
%V 2011
%U http://geodesic.mathdoc.fr/item/EJDE_2011__2011__a37/
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%F EJDE_2011__2011__a37
Turki,  Sameh. Existence of continuous positive solutions for some nonlinear polyharmonic systems outside the unit ball. Electronic journal of differential equations, Tome 2011 (2011). http://geodesic.mathdoc.fr/item/EJDE_2011__2011__a37/