Positive solutions for semi-positone systems in an annulus

We study existence and multiplicity results for positive solutions for semi-linear elliptic systems of the form (p(t)u')' = -lambda f(u, v)p(t); t is an element of (a, b) (p(t)v')' = -lambda g(u, v)p(t); t is an element of (a, b) u(a) = 0 = u(b), v(a) = 0 = v(b) where lambda > 0 is a parameter, p : [a,b] --> R is continuous with p > 0 on [a,b] and g,f : [0,infinity) x [0,infinity) --> R are continuous such that f(u, v) greater than or equal to -(M/2), g(u, v) greater than or equal to -(M/2) for every (u., v) is an element of [0, infinity) x [0, infinity) for some M > 0. Our proofs are based on fixed point theory in a cone. Our results extend existence results for single semi-positone equations to semi-positone systems. We also establish a multiplicity result which is new even in the case of single equations.