Boundary blow-up rate of solutions to elliptic cooperative systems

摘要

This paper shows the existence, uniqueness, and boundary blow-up rate of large solution of cooperative systems of the form -Delta u1=lambda 1u1+a1u2q1-b1(x)u1p1,-Delta u2=lambda 2u2+a2u1q2-b2(x)u2p2 in a bounded smooth domain omega subset of R-N, b(i)(x) is nonnegative weight function that can be singular on partial differential omega, and the exponents verify lambda(i)is an element of R,a(i)>0,p(i)>1,q(i)>0 for i=1,2, and q(1)q(2)1p(2).