Existence and multiplicity of positive solutions for semilinear ellipticsystems with Sobolev critical exponents

摘要

In this paper, we study the existence and multiplicity of positive solutions to the followingsystem —Au =(u, v) + eg(x),v = g(u, v) Eh(x) in Q; u, v > 0 in S2; andu = v = 0 on a Q, where S2 is a bounded smooth domain in RN; F E C1((R-1-)2, R±) ispositively homogeneous of degree 1,1; g, h E CI (S2) (01; and E is a positive parameter.Using sub—supersolution method, we prove the existence of positive solutions for theabove problem. By means of the variational approach, we prove the multiplicity of positivesolutions for the above problem with it E (2, 2* J.