Multiple positive solutions for functional dynamic equations on time scales

In this paper, we study the following functional dynamic equation on time scales: .u .t// r C a.t/f .u.t/; u. .t/// D 0; t 2 .0; T /T ; u.t/ D ʹ.t/; t 2 [􀀀r; 0/T ; u.0/ 􀀀 B0.u .0// D 0; u .T / D 0; where V R ! R is an increasing homeomorphism and a positive homomorphism and .0/ D 0. By using the well-known Leggett Williams fixed point theorem, existence criteria for multiple positive solutions are established. An example is also given to illustrate the main results.