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This paper considers the system of nonlinear Dirichlet boundary value problems Here L is a strongly, uniformly elliptic linear partial differential operator, A, p. are real parameters, and /, g: R2 -> R are smooth with /(0,0) = 0 = 9(0,0). A detailed analysis of the solution set to the system is given from the point of view of several parameter bifurcation theory.doi:10.2307/2000130 fatcat:dz444kx3efcjtfnky7opc7zi6m