Positive solutions of nonlinear operator equations with sign-changing kernel and its applications

In this paper, the existence of positive solutions of nonlinear operator equation u=λTuu=λTu are studied, where λ>0λ>0 is a parameter, T is a compact operator with sign-changing kernel. By using the Leray–Schauder degree theory, the existence of positive solutions of nonlinear operator equations with sign-changing kernel are obtained. The obtained abstract theorem can be applied easily, to illustrate this point the paper also introduces some applications.