Twin Positive Solutions of Second-Order m-Point Boundary Value Problem with Sign Changing Nonlinearities

In this paper, we study second-order m-point boundary value problem ( u 00(t) +a(t)u 0 (t) + f(t,u) = 0, 0 ? t ? 1, u 0 (0) = 0, u(1) = ? k i=1 aiu(?i)?? m?2 i=k+1 aiu(?i), where ai > 0(i = 1,2,...,m?2),0 < ? k i=1 ai ?? m?2 i=k+1 ai < 1,0 < ?1 < ?2 < ··· < ?m?2 < 1, a ?C([0,1],(??,0)) and f is allowed to change sign. We show that there exist two positive solutions by using Leggett-Williams fixed-point theorem. The conclusions in this paper essentially extend and improve some known results. 2010 Mathematics Subject Classification: 34B15, 34B25