On the number of positive solutions of a nonlinear algebraic system

Abstract: In this paper, we study the nonlinear algebraic system of the formwhere λ >0 is a parameter, x and F(x) denote the column vectors:respectively with f k : R → R, k ∈{1,2,…, n}=[1, n] and n is a positive integer. A =(a ij ) 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). [Copyright &y& Elsevier]