A $(k, n − k)$ Conjugate Boundary Value Problem with Semipositone Nonlinearity (Communications in Mathematical Research, 2021)
The existence of positive solution is proved for a $(k, n − k)$ conjugateboundary value problem in which the nonlinearity may make negative values andmay 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 theHammerstein integral equation and the Krasnosel'skii's cone expansion-compressiontechnique.
Keywords: higher order ordinary differential equation; boundary value problem; semipositone nonlinearity; positive solution.