Resumen de On a reaction-diffusion system involving the critical exponent
In this paper we study the existence and multiplycity of the nontrivial solutions for the following elliptic system with Dirichlet boundary conditions and critical nonlinearity { -D u = l u + W(x) u |u|2* - 2 -kv -D v = d u - g v u = v = 0 in W in W in ¶ W where WÌRN (N ³ 3) is a bounded regular domain, W(×) Î Lµ (W) with the property that there exists h >0 such that W(×) ³h a.e. in W and l,d,g are real parameters. We show that the number of nontrivial solutions, in a left neighbourhood of each lÙ j, j=1,2,..., is at least twice the multiplicity of lÙ j, where the set {lÙ j}j ÎN* represents the spectrum of a certain integro-differential operator.
