Global bifurcation of positive solutions of a second-order periodic boundary value problem with indefinite weight

Abstract

In this paper, we are concerned with the global structure and stability of positive solutions of periodic boundary value problem − u ″ ( t ) + q ( t ) u ( t ) = λ a ( t ) f ( u ( t ) ) , 0 < t < 2 π , u ( 0 ) = u ( 2 π ) , u ′ ( 0 ) = u ′ ( 2 π ) , where q ∈ C ( R , [ 0 , ∞ ) ) is of periodic 2 π and q ( t ) ≢ 0 , t ∈ [ 0 , 2 π ] ; a ∈ C ( R , R ) is of periodic 2 π and changes sign. The proof of our main results are based on bifurcation techniques.