Open AccessMultiple Positive Solutions of m-Point BVPs for Third-Order p-Laplacian Dynamic Equations on Time Scales
Author(s) -
Li-Hua Bian,
Xiping He,
HongRui Sun
Publication year - 2009
Publication title -
advances in difference equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.67
H-Index - 51
eISSN - 1687-1847
pISSN - 1687-1839
DOI - 10.1155/2009/262857
Subject(s) - mathematics , ordinary differential equation , partial differential equation , dynamic equation , mathematical analysis , order (exchange) , third order , p laplacian , differential equation , boundary value problem , physics , nonlinear system , philosophy , theology , quantum mechanics , finance , economics
This paper is concerned with the existence of multiple positive solutions for the third-order p-Laplacian dynamic equation (ϕp(uΔ∇(t)))∇+a(t)f(t,u(t),uΔ(t))=0,t∈[0,T]𝕋 with the multipoint boundary conditions uΔ(0)=uΔ∇(0)=0,u(T)+B0(∑i=1m−2biuΔ(ξi))=0, where ϕp(u)=|u|p−2u with p>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-order p-Laplacian dynamic equation but also the nonlinear term f is involved with the first-order delta derivative of the unknown function