Resumen de On a reaction-diffusion system involving the critical exponent

Nicolae Tarfulea

• 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.