Full paper in PDF:
$%N. Ţarfulea, On a reaction-diffusion system involving the critical exponent, Rev. Mat. Complut. 11 (1998), no. 2, 461472.%$

On a Reaction-Diffusion System Involving the Critical Exponent
Nicolae ŢARFULEA
Department of Mathematics
University of Craiova
1100 Craiova Romania

Received: February 12, 1997
Revised: May 7, 1998
ABSTRACT

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

  -Du = cu+ W (x)u|u|2*-2- kv  in _O_,
{ -Dv = du- gv               in _O_,

  u= v =0                    in @_O_,

where _O_< RN  (N > 3  ) is a bounded regular domain, W(.) (- Lo o (_O_)  with the property that there exists j > 0  such that W(.)> j  a.e. in _O_  and c  , d  , g  are real parameters. We show that the number of nontrivial solutions, in a left neighborhood of each cj  , j =1,2,...  , is at least twice the multiplicity of cj  , where the set {cj}j (- N* represents the spectrum of a certain integro-differential operator.

1991 Mathematics Subject Classification: 35J55, 35J50.