Existence and multiplicity of average-positive solutions to periodic boundary value problem with sign-changing Green's function

Abstract

This paper deals with the periodic boundary value problem u^”+ρ^2 u=g(t)f(u),0 0 is a constant satisfying ρ≠2nπ/T,n=1,2,… and the associated Green’s function changes sign when ρ>π/T. The existence and multiplicity results for average-positive solutions are established by using the fixed point index theory of cone mapping.