Triple positive pseudo-symmetric solutions of three-point BVPs for [formula omitted]-Laplacian dynamic equations on time scales

Abstract

Let T be a time scale such that 0 , T ∈ T . We consider the three-point boundary value problem for p -Laplacian dynamic equations on time scales T of the form ( ϕ p ( u Δ ( t ) ) ) ∇ + h ( t ) f ( t , u ( t ) ) = 0 for t ∈ ( 0 , T ) T with boundary conditions u ( 0 ) = 0 , u ( η ) = u ( T ) , where T is symmetric in [ η , T ] T and ϕ p ( u ) = | u | p − 2 u with p > 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.