Nonexistence of positive solutions for a class of semilinear elliptic systems

We consider the system -Delta u = lambda f(v); x is an element of Omega -Delta v = mu g(u); x is an element of Omega u = 0 = v; x is an element of delta Omega where Omega is a ball in R-N, N >= 1 and delta Omega is its boundary, A, it are positive parameters bounded away from zero, and f, g are smooth functions that are negative at the origin and grow at least linearly at infinity. We establish the nonexistence of positive solutions when lambda mu is large. Our proofs depend on energy analysis and comparison methods.