Electronic Journal of Differential Equations,
Vol. 2011 (2011), No. 81, pp. 1-13.
Title: Existence of continuous positive solutions for some
nonlinear polyharmonic systems outside the unit ball
Author: Sameh Turki (Faculte des Sciences de Tunis, Tunisia)
Abstract:
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.
Submitted May 23, 2011. Published June 21, 2011.
Math Subject Classifications: 34B27, 35J40.
Key Words: Polyharmonic elliptic system; Positive solutions;
Green function; polyharmonic Kato class.