Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: Existence of positive solutions for nonlocal second-order boundary value problem with variable parameter in Banach spaces | Zhang Fixed Point Theory and Applications 2011 2011 43 http content 2011 1 43 RESEARCH Fixed Point Theory and Applications a SpringerOpen Journal Open Access Existence of positive solutions for nonlocal second-order boundary value problem with variable parameter in Banach spaces Peiguo Zhang Correspondence pgzhang0509@ Department of Elementary Education Heze University Heze 274000 Shandong People s Republic of China Abstract By obtaining intervals of the parameter l this article investigates the existence of a positive solution for a class of nonlinear boundary value problems of second-order differential equations with integral boundary conditions in abstract spaces. The arguments are based upon a specially constructed cone and the fixed point theory in cone for a strict set contraction operator. MSC 34B15 34B16. Keywords boundary value problem positive solution fixed point theorem measure of noncompactness 1 Introduction The existence of positive solutions for second-order boundary value problems has been studied by many authors using various methods see 1-6 . Recently the integral boundary value problems have been studied extensively. Zhang et al. 7 investigated the existence and multiplicity of symmetric positive solutions for a class of Ji-Laplacian fourth-order differential equations with integral boundary conditions. By using Mawhin s continuation theorem some sufficient conditions for the existence of solution for a class of second-order differential equations with integral boundary conditions at resonance are established in 8 . Feng et al. 9 considered the boundary value problems with one-dimensional 1D Ji-Laplacian and impulse effects subject to the integral boundary condition. This study in this article is motivated by Feng and Ge 1 who applied a fixed point theorem 10 in cone to the second-order differential equations. x t f t x t 0 0 t 1 x 0 Jo g t x t dt x 1 0. Let E be a real Banach space with norm and P
