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In this paper, we study the global structure of positive solutions of periodic boundary value problems $$textstylebegin{cases} -uu0027u0027(t)+q(t)u(t)=lambda h(t)f(u(t)), quad tin (0,2pi ),  u(0)=u(2pi ), quadquad uu0027(0)=uu0027(2pi ), end{cases} $$where (qin C([0,2pi ], [0, +infty ))) with (qnot equiv 0), (fin C(mathbb{R},mathbb{R})), the weight (hin C[0,2pi ]) is a sign-changing function, λ is a parameter. We prove the existence of three positive solutions when (h(t)) has n positive humps separated by (n+1) negative ones. The proof is based on the bifurcation method.

Three positive solutions for second-order periodic boundary value problems with sign-changing weight