On the existence of many solutions for a class of superlinear elliptic systems

We seek multiple solutions to systems of semilinear elliptic equations of the type - DeltaU(chi) = delH(chi; U(chi)) chi is an element of Omega U(x) = 0 chi is an element of partial derivative Omega, where Omega subset of R-N (N greater than or equal to 1) is a bounded regular domain and U = (u(1), u(2)): Omega --> R-2. For a class of potentials where the variables are strongly coupled as in the model H(chi; u(1), u(2)) = \u(1)\ (alpha1) \u(2)\ (alpha2) with alpha (1) > 1, we provide the existence of nine nontrivial solutions characterized by sign properties of each component. (C) 2000 Academic Press.