Positive solutions of nonlinear operator equations with sign-changing kernel and its applications
Abstract In this paper, the existence of positive solutions of nonlinear operator equation u = λ Tu are studied, where λ > 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.