A $(k, n − k)$ Conjugate Boundary Value Problem with Semipositone Nonlinearity
DOI:
https://doi.org/10.13447/j.1674-5647.2015.01.06Keywords:
higher order ordinary differential equation, boundary value problem, semipositone nonlinearity, positive solution.Abstract
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'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'skii's cone expansion-compression technique.