Three positive solutions for higher order <f>m</f>-point boundary value problems

In this paper, we consider the existence of at least three positive solutions for the <f>2n</f>th order <f>m</f>-point boundary value problem y(2n)(t)=f<fen><cp type="lpar" STYLE="S">t,y(t),y″(t),…,y(2(n−1))(t)<cp type="rpar" STYLE="S"></fen>, 0&les;t&les;1,y(2i)(0)=0, y(2i)(1)=∑lower limit j=1, upper limit m−2 kijy(2i)(ξj), 0&les;i&les;n−1, where <f>kij>0</f> (<f>i=0,1,…,n−1</f>; <f>j=1,2,…,m−2</f>), <f>0<ξ1<ξ2<⋯<ξm−2<1</f>. The associated Green''s function for the higher order <f>m</f>-point boundary value problem is first given, and growth conditions are imposed on <f>f</f> which yield the existence of multiple positive solutions by using the Leggett–Williams fixed point theorem. [Copyright &y& Elsevier]