Multiple Positive Solutions to Multipoint Boundary Value Problem for a System of Second-Order Nonlinear Semipositone Differential Equations on Time Scales

Abstract

We study a system of second-order dynamic equations on time scales(p1u1∇)Δ(t)-q1(t)u1(t)+λf1(t,u1(t),u2(t))=0,t∈(t1,tn),(p2u2∇)Δ(t)-q2(t)u2(t)+λf2(t,u1(t),u2(t))=0, satisfying four kinds of different multipoint boundary value conditions,fiis continuous and semipositone. We derive an interval ofλsuch that anyλlying in this interval, the semipositone coupled boundary value problem has multiple positive solutions. The arguments are based upon fixed-point theorems in a cone.