Existence Of Positive Solutions For Some Classes Of Non-linear First-order Periodic Boundary Value Problems

In this paper,we study the existence of positive solutions for some classes of non-linear first-order periodic boundary value problems by using topological degree and bifurcation theory.The main results are described as follows:1.The global structure of positive solutions of boundary value problem for first order ordinary differential equati(?)is studied by bifurcation theory,where f?C([0,1]×R,R),q?C([0,1],[0,?)),a?C([0,1],(0,?))and A is a positive parameter.In this chapter,after adding oscilla-tion condition to the non-linear term f,the connected branches of positive solutions also begin to oscillate,and the oscillation amplitude is bounded and does not tend to zero.The main results are inspired by B.P.Rynne Proc.American Math.So-ci.,1999],and supplement the results of G.P.Shi[Appl.Math.Comput.,2004]and R.Y.Ma and L.Zhang[Bound.Value Probl.,2015].2.By using the theory of topological degree and bifurcation theory,we study the existence of positive solutions of problem(?)under the condition that f takes negative value at u?0 and satisfies the conditions of asymptotically linear growth,superlinear growth or sublinear growth at infinity,where f?C([0,1]x R,R),f(t,0)<0,t ? 0,1],? can variable sign,? is a positive parameter.The main results generalize the results of H.Q.Lu[J.of Appl.Math.,2012].