Triple positive pseudo-symmetric solutions of three-point BVPs for image-Laplacian dynamic equations on time scales Original Research Article

Let TT be a time scale such that 0,T∈T0,T∈T. We consider the three-point boundary value problem for pp-Laplacian dynamic equations on time scales TT of the form View the MathML source(ϕp(uΔ(t)))∇+h(t)f(t,u(t))=0 for t∈(0,T)Tt∈(0,T)T with boundary conditions u(0)=0u(0)=0, u(η)=u(T)u(η)=u(T), where TT is symmetric in [η,T]T[η,T]T and ϕp(u)=|u|p−2uϕp(u)=|u|p−2u with p>1p>1. By using a pseudo-symmetric technique and the five-functionals fixed-point theorem, we prove that the boundary value problem has at least three positive pseudo-symmetric solutions under some assumptions. As an application, an example is given to illustrate the result.