Existence of continuous positive solutions for some nonlinear polyharmonic systems outside the unit ball

• Main Author: Sameh Turki
• Format: Article
• Language: English
• Published: Texas State University 2011-06-01
• Series: Electronic Journal of Differential Equations
• Subjects: Polyharmonic elliptic system; Positive solutions; Green function; polyharmonic Kato class
• Online Access: http://ejde.math.txstate.edu/Volumes/2011/81/abstr.html

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 $mgeq 1$). 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.