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

Abstract EN

Let ? be a time scale with 0,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 ?, uΔΔ(t)+f(t,uσ(t))=0, t∈[0,T]?, u(0)=u(σ2(T))=0, which is not necessarily linearizable.

Our approaches are based on topological degree theory and global bifurcation techniques.