Abstract In this article we study several classes of sum operator equations on ordered Banach spaces and present some new existence and uniqueness results of positive solutions, which extend the existing corresponding results. Moreover, we establish some pleasant properties of nonlinear eigenvalue problems for several classes of sum operator equations. As applications, we utilize the main results obtained in this paper to study two classes nonlinear problems; one is the integral equation u(t)=λ∫abG(t,s)f(s,u(s))ds , where f and G are both nonnegative, λ>0 is a parameter; the other is the elliptic boundary value problem for the Lane-Emden-Fowler equation −Δu=λf(x,u) , u(x)>0 in Ω, u(x)=0 on ∂ Ω, where Ω is a bounded domain with smooth boundary in RN ( N≥1 ), λ>0 and f(x,u) is allowed to be singular on ∂ Ω. The new results on the existence and uniqueness of positive solutions for these problems are given, which complement the existing results of positive solutions for these problems in the literature. MSC: 47H10, 47H07, 45G15, 35J60, 35J65.

	Year	Citations

About

Top Concepts