TY - JOUR
T1 - A $(k, n − k)$ Conjugate Boundary Value Problem with Semipositone Nonlinearity
AU - Yao , Qingliu
JO - Communications in Mathematical Research 
VL - 1
SP - 51
EP - 61
PY - 2021
DA - 2021/05
SN - 31
DO - http://doi.org/10.13447/j.1674-5647.2015.01.06
UR - https://global-sci.org/intro/article_detail/cmr/18946.html
KW - higher order ordinary differential equation, boundary value problem,
semipositone nonlinearity, positive solution.
AB - <p style="text-align: justify;">The existence of positive solution is proved for a $(k, n − k)$ conjugate
boundary value problem in which the nonlinearity may make negative values and
may be singular with respect to the time variable. The main results of Agarwal et al.
(Agarwal R P, Grace S R, O&#39;Regan D. Semipositive higher-order differential equations. Appl. Math. Letters, 2004, 14: 201–207) are extended. The basic tools are the
Hammerstein integral equation and the Krasnosel&#39;skii&#39;s cone expansion-compression
technique.</p>