EXISTENCE OF POSITIVE SOLUTIONS FOR SUPERLINEAR SEMIPOSITONE $m$-POINT BOUNDARY-VALUE PROBLEMS

Proceedings of the Edinburgh Mathematical Society

Ruyun Ma¹ 

关键词: multipoint boundary-value problems;    positive solutions;    fixed-point theorem;    cones;   

DOI  :  10.1017/S0013091502000391

学科分类：数学（综合）

来源: Cambridge University Press

【 摘 要 】

In this paper we consider the existence of positive solutions to the boundary-value problemsegin{align*} (p(t)u')'-q(t)u+lambda f(t,u)amp=0,quad rlttltR, \[2pt] au(r)-bp(r)u'(r)amp=sum^{m-2}_{i=1}alpha_iu(xi_i), \ cu(R)+dp(R)u'(R)amp=sum^{m-2}_{i=1}eta_iu(xi_i), end{align*}where $lambda$ is a positive parameter, $a,b,c,din[0,infty)$, $xi_iin(r,R)$, $alpha_i,eta_iin[0,infty)$ (for $iin{1,dots m-2}$) are given constants satisfying some suitable conditions. Our results extend some of the existing literature on superlinear semipositone problems. The proofs are based on the fixed-point theorem in cones.AMS 2000 Mathematics subject classification: Primary 34B10, 34B18, 34B15

【 授权许可】

Unknown