We study the existence of a positive radial solution to the nonlinear eigenvalue problem (Formula presented.) in (Formula presented.) in (Formula presented.) as (Formula presented.), where (Formula presented.) is a parameter, (Formula presented.) is the Laplace operator, (Formula presented.) are such that (Formula presented.). Here (Formula presented.) are (Formula presented.) functions such that they are negative at the origin (semipositone) and superlinear at infinity. We establish the existence of a positive solution for λ small via degree theory and rescaling arguments. We also discuss a non-existence result for λ≫1 for the single equations case. © 2014, Abebe et al.; licensee Springer.