Volume 31, Issue 1
A $(k, n − k)$ Conjugate Boundary Value Problem with Semipositone Nonlinearity

Commun. Math. Res., 31 (2015), pp. 51-61.

Published online: 2021-05

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• 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.

• Keywords

higher order ordinary differential equation, boundary value problem, semipositone nonlinearity, positive solution.

34B15, 35B18

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@Article{CMR-31-51, author = {Qingliu and Yao and and 18599 and and Qingliu Yao}, title = {A $(k, n − k)$ Conjugate Boundary Value Problem with Semipositone Nonlinearity}, journal = {Communications in Mathematical Research }, year = {2021}, volume = {31}, number = {1}, pages = {51--61}, 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.

}, issn = {2707-8523}, doi = {https://doi.org/10.13447/j.1674-5647.2015.01.06}, url = {http://global-sci.org/intro/article_detail/cmr/18946.html} }
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 -

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.

Qingliu Yao. (2021). A $(k, n − k)$ Conjugate Boundary Value Problem with Semipositone Nonlinearity. Communications in Mathematical Research . 31 (1). 51-61. doi:10.13447/j.1674-5647.2015.01.06
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