数学物理学报(英文版) ›› 2001, Vol. 21 ›› Issue (2): 189-195.
王汝发, 马如云, 任立顺
WANG Ru-Fa, MA Ru-Yun, REN Li-Shun
摘要：
We study the existence of positive solutions to the boundary value problem (p(t)u′)′ + f(t, u) + e(t, u) = 0, r < t < R, au(r) − bp(r)u′(r) = 0, cu(R) + dp(R)u′(R) = 0,where f and e : [r,R] × [0,1) ! R are two continuous functions satisfying f 0 and |e| M for some M > 0. We show that there exists at least one positive solution in the following two cases: (i) f is superlinear at infinity and > 0 is small enough; (ii) f is sublinear at infinity and > 0 is large enough. Our proofs are based on fixed point theorems in a cones.