数学物理学报（英文版）
數學物理學報（英文版）
수학물이학보（영문판）
ACTA MATHEMATICA SCIENTIA
2014年
6期
1795-1810
,共16页
boundary value problems%positive solutions%lower and upper solutions%com-parison theorem
We mainly study the existence of positive solutions for the following third order singular multi-point boundary value problem???????x(3)(t)+f(t, x(t), x′(t))=0, 0<t<1, x(0)?m1X i=1αix(ξi)=0, x′(0)?m2X i=1βi x′(ηi )=0, x′(1)=0, where 0≤αi≤mP1 i=1αi<1, i=1, 2, · · · , m1 , 0<ξ1<ξ2<· · ·<ξm1 <1, 0≤βj ≤mP2 i=1βi<1, j = 1, 2, · · · , m2, 0 < η1 < η2 < · · · < ηm2 < 1. And we obtain some necessary and su?cient conditions for the existence of C1[0, 1] and C2[0, 1] positive solutions by constructing lower and upper solutions and by using the comparison theorem. Our nonlinearity f (t, x, y) may be singular at x, y, t=0 and/or t=1.
