Multiple Positive Solutions of m-Point BVPs for Third-Order p-Laplacian Dynamic Equations on Time Scales. (27th October 2009) - Bian, Li-Hua; He, Xi-Ping; Sun, Hong-Rui
Abstract : This paper is concerned with the existence of multiple positive solutions for the third-orderp -Laplacian dynamic equation( ϕ p ( u Δ ∇ ( t ) ) ) ∇ + a ( t ) f ( t, u ( t ), u Δ ( t ) ) = 0, t ∈ [ 0, T ] 𝕋 with the multipoint boundary conditionsu Δ ( 0 ) = u Δ ∇ ( 0 ) = 0, u ( T ) + B 0 ( ∑ i = 1 m − 2 b i u Δ ( ξ i ) ) = 0, whereϕ p ( u ) = | u | p − 2 u withp > 1 . Using the fixed point theorem due to Avery and Peterson, we establish the existence criteria of at least three positive solutions to the problem. As an application, an example is given to illustrate the result. The interesting points are that not only do we consider third-orderp -Laplacian dynamic equation but also the nonlinear termf is involved with the first-order delta derivative of the unknown function.