Positive Solutions Of Second-order Periodic Boundary Value Problems With A Singular Nonlinearity

In this paper, by using the Schauder’s fixed point theorem, the Rabinowitz global bifurcation theorem and topological degree theory, we discuss the existence of positive solutions of several kinds of second order periodic boundary value problems.It is divided into three sections.In Section1and2, by using the Schauder’s fixed point theorem, we investigate the existence of positive solutions for second-order periodic boundary value problems where a, c∈L1(0, ω),f∈Car([0,ω]×R+,R+) and may be singular at u=0. Under some suitable conditions on the nonlinearity f, we show that the boundary value problem has at least one positive solutions. Our main results extend and improve the corresponding ones of P. J. Torres [J. Diff. Eqns.,2007].In section3, by using the Rabinowitz global bifurcation theorem and topological degree theory, we study the global structure of positive solutions of the second order periodic boundary value problems where a∈C([0,ω],R+), f∈C([0,ω],R+), and λ>0is a parameter. Our results extend and improve the corresponding ones of D. Jiang [Acta Math. Sci.,1998] and R. Ma et al.[Boundary value problem,2010].