The existence results of positive solutions are obtained for the fourth-order periodic boundary value problemu(4)−βu′′+αu=f(t,u,u′′),0≤t≤1,u(i)(0)=u(i)(1), i=0,1,2,3, wheref:[0,1]×ℝ+×ℝ→ℝ+is continuous,α,β∈ℝ,and satisfy0<α<((β/2)+2π2)2,β>−2π2,(α/π4)+(β/π2)+1>0. The discussion is based on the fixed point index theory in cones.
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