Existence of Positive Solutions for a Fourth-Order Periodic Boundary Value Problem

Abstract EN

The existence results of positive solutions are obtained for the fourth-order periodic boundary value problem u(4)−βu′′+αu=f(t,u,u′′), 0≤t≤1, u(i)(0)=u(i)(1), i=0,1,2,3, where f:[0, 1]×R+×R→R+ is continuous, α, β∈R, and satisfy 0<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.