On the number of positive solutions of a nonlinear algebraic system

In this paper, we study the nonlinear algebraic system of the formequation(E)x=λAF(x),x=λAF(x),where λ > 0 is a parameter, x and F(x) denote the column vectors:col(x1,x2,…,xn)andcol(f1(x1),f2(x2),…,fn(xn)),respectively with fk : R → R, k ∈ {1, 2, … , n} = [1, n] and n is a positive integer. A = (aij)n × n is an n × n matrix and all its entries are positive numbers.Many problems in various areas such as difference equations, boundary value problems, dynamical networks, stochastic process, numerical analysis etc. can be converted to system (E). Applying fixed point theorems, we prove results on existence, uniqueness, multiplicity and nonexistence of positive solutions for (E).