Positive solutions of M-point boundary value problem for second-order dynamic equations on time scales†

^†This project is supported by the Tianyuan Youth Grant of China (No. 10626004), the Excellent Younger Teacher Program of Jiangsu Province in China (QL200613) and Xuzhou Normal University, Jiangsu Government Scholarship Program and the Natural Science Foundation of Xuzhou Normal University (Nos. 07XLB01, 06XLA03, KY2006118).

Abstract

This paper deals with the existence of multiple positive solutions for second-order dynamic equations on time scales

with multi-point boundary conditions

where T is a time scale, , , . By using Green's function and the Leggett–Williams fixed point theorem in an appropriate cone, the existence of at least three positive solutions of the problem is obtained.

Keywords:

• multi-point boundary value problem
• dynamic equations
• time scales
• positive solutions
• Green's function

Keywords:

• MR (2000)

Keywords:

• 34B15
• 39A10

Acknowledgements

The authors wish to express their thanks to the referee for his or her comments and careful corrections.

Notes

^†This project is supported by the Tianyuan Youth Grant of China (No. 10626004), the Excellent Younger Teacher Program of Jiangsu Province in China (QL200613) and Xuzhou Normal University, Jiangsu Government Scholarship Program and the Natural Science Foundation of Xuzhou Normal University (Nos. 07XLB01, 06XLA03, KY2006118).

1. [email protected]

Additional information

Notes on contributors

Xiaojie Lin

1