On positive solutions of nonlinear elliptic eigenvalue problems

Suppose Ω is a bounded region in Rⁿ. In this paper we investigate the equation Lu=λF(x, u), u|_∂Ω=0 where L is an elliptic partial differential operator and V 3 F(x, t) is a positive function on Ωx R¹ which may have jump discontinuities with respect to t. We show that if certain conditions are satisfied there exists an unbounded continuum Λ of solutions (γ, u), with u(x)≥0, in the space R¹×S. Here S is a Banach space of real valued functions such as(Formula presented.)