Positive solutions of fourth-order periodic boundary value problems Original Research Article

In this paper the existence results of positive solutions are obtained for fourth-order periodic boundary value problem u(4)−βu″+αu=f(t,u),0⩽t⩽1, u(i)(0)=u(i)(1),i=0,1,2,3, where View the MathML source is continuous, View the MathML source and satisfy 0<α<(β/2+2π2)2,β>−2π2,α/π4+β/π2+1>0. The discussion is based on a new maximum principle for operator View the MathML source in periodic boundary condition and fixed point index theory in cones.