### Existence of positive solutions to a semipositone second-order boundary value problem

WEI Jin-ying, WANG Su-yun, LI Yong-jun

1. School of Mathematics, Lanzhou City University, Lanzhou 730070, Gansu, China
• Published:2019-10-12

Abstract: We consider the existence of positive solutions to the boundary value problemu″(t)+c(t)u+λf(t,u)=0, 0λ>0, c(·)∈C［0,1 satisfies -∞π2 for t∈［0,1, f:［0,1］×R+→R is continuous function and satisfies f≥-L, L>0 is a constant. By investigating the sign property of the Green function of the associated linear boundary value problem, we show the existence of positive solutions of semipositone problems. The proof of the main result is based on Krasnoselskii fixed point theorems in cone.

CLC Number:

• O175.8
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