ABSTRACT
The study of non-negative solutions to the nonlinear equations, especially the ordinary or partial differential equations and integral equations, is a very important problem in nonlinear functional analysis. The non-negativity condition can be described by a closed convex subset P in a Banach space which satisfies λP ⊂ P for all λ ≥ 0 and P ∩−P = {0}. We are interested in solving the equation Tx = y in P . The fixed point index theory has proved to be a useful tool in studying such an equation.
