Existence and uniqueness of solutions for the second order periodic-integrable boundary value problem

Springer Science and Business Media LLC - Tập 2017 - Trang 1-13 - 2017
Xue Feng1,2, Fuzhong Cong1,2
1Institute of Mathematics, Jilin University, Changchun, China
2Fundamental Department, Aviation University of Air Force, Changchun, China

Tóm tắt

This paper is mainly devoted to studying one kind of the second order differential equation. Under periodic-integrable boundary value condition, the existence of the solutions of this equation is discussed by the method of the operator theory and the Schauder fixed point theorem.

Tài liệu tham khảo

Yang, Z: Positive solutions to a system of second-order nonlocal boundary value problems. Nonlinear Anal. 62, 1251-1265 (2005) Yao, Q: Positive solutions of nonlinear second-order periodic boundary value problems. Appl. Math. Lett. 20, 583-590 (2007) Zhang, J, Xu, C: Nonlinear periodic boundary value problem for a second order ordinary differential equations. Nonlinear Anal., Theory Methods Appl. 32, 881-890 (1998) Song, G, Zhao, Y, Sun, X: Integral boundary value problem for first order impulsive integral-differential equations of mixed type. Appl. Math. 235, 2928-2935 (2011) Feng, MQ, Ji, DH, Ge, WG: Positive solutions for a class of boundary value problem with integral boundary conditions in Banach spaces. J. Comput. Appl. Math. 222, 351-363 (2008) Li, Y: Positive solutions for second order boundary value problems with sign changing nonlinear term. J. Math. Anal. Appl. 282, 232-240 (2003) Hua, HT, Cong, FZ, Cheng, Y: Notes on existence and uniqueness of solution for second order periodic-integaral boundary value problems. Appl. Math. Lett. 25, 2423-2428 (2012) Cong, FZ: Existence and uniqueness of periodic solutions for \((2n+1)\)th-order ordinary differential equations. Appl. Math. Lett. 17, 727-732 (2004) Cong, FZ: Periodic solutions for second order differential equations. Appl. Math. Lett. 18, 957-961 (2005)