On positive solutions for classes of p-Laplacian semipositone systems

We study positive solutions for the system -Delta(p)u = lambdaf(v) in Omega -Delta(p)v = lambdag(u) in Omega u = 0 = v on partial derivativeOmega where lambda > 0 is a parameter, Deltap denotes the p-Laplacian operator defined by Deltap(z) := div(\delz\(p-2del)z) for p > 1 and Omega is a bounded domain with smooth boundary. Here f, g is an element of C[0,infinity) belong to a class of functions satisfying lim(z-->infinity) f(z)/z(p-1) = 0, lim(z-->infinity) g(z)/z(p-1) = 0. In particular, we discuss the existence of radial solutions for large lambda when Omega is an annulus. For a general bounded region Omega, we also discuss a non-existence result when f(0) < 0 and g(0) < 0.