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$%N. Ţarfulea, On a reaction-diffusion system involving the critical exponent, Rev. Mat. Complut. 11 (1998), no. 2, 461–472.%$

In this paper we study the existence and multiplicity of the nontrivial solutions for the following elliptic system with Dirichlet boundary conditions and critical nonlinearity

where () is a bounded regular domain, with the property that there exists such that a.e. in and , , are real parameters. We show that the number of nontrivial solutions, in a left neighborhood of each , , is at least twice the multiplicity of , where the set represents the spectrum of a certain integro-differential operator.

1991 Mathematics Subject Classification: 35J55, 35J50.