Bifurcation from Interval and Positive Solutions of a Nonlinear Second‐Order Dynamic Boundary Value Problem on Time Scales

Abstract

Let 𝕋 be a time scale with 0, T ∈ 𝕋. We give a global description of the branches of positive solutions to the nonlinear boundary value problem of second‐order dynamic equation on a time scale 𝕋, uΔΔ(t) + f(t, uσ(t)) = 0, t ∈ [0, T] 𝕋, u(0) = u(σ2(T)) = 0, which is not necessarily linearizable. Our approaches are based on topological degree theory and global bifurcation techniques.