Positive Solutions Of Second-order Nonlinear Boundary Value Problem With Sign-changing Green’s Function

In this thesis,we investigate the existence of positive solutions of second-order nonlinear boundary value problem with sign-changing Green’s function,(?)where f:[0,∞)→R,g:[0,2π]→R.By judging the sign of Green’s function in this thesis,and giving some inequality conditions of nonlinear function f and g,the Leray-Schauder fixed point theorem is used to ensure the existence of positive solutions of the boundary value problem.Suppose that:(H1)α≠β,α≠0,β≠0,α≠±1,β≠±1.(H2)f:[0,∞)→R is continuous,and f(0)>0.(H3)g∈L∞(0,2π),g>-0(g≥0,a.e.t∈[0,2π],and g(t)is not equal to zero almost everywhere in the whole interval).(H4)Defining:(?)There exists a constant ε>0,such that(?),then the boundary value problem has positive solutions.Under the hypotheses(H1)and(H2),suppose that:(H5)g ∈L1[0,2π]and g(t)is not nearly equal to zero everywhere for any interval in[0,2π].There exists a constant ε>0,such that,(?)where Then the boundary value problem has positive solutions.The existence of positive solutions on the boundary value problem under different assumptions is mainly discussed in the thesis,and the examples are provided to illustrate the application of the corresponding theorems respectively.