EXISTENCE, MULTIPLICITY AND UNIQUENESS RESULTS FOR A SECOND ORDER M-POINT BOUNDARY VALUE PROBLEM

- Journal title : Bulletin of the Korean Mathematical Society
- Volume 41, Issue 3, 2004, pp.483-492
- Publisher : The Korean Mathematical Society
- DOI : 10.4134/BKMS.2004.41.3.483

Title & Authors

EXISTENCE, MULTIPLICITY AND UNIQUENESS RESULTS FOR A SECOND ORDER M-POINT BOUNDARY VALUE PROBLEM

Feng, Yuqiang; Liu, Sang-Yang;

Feng, Yuqiang; Liu, Sang-Yang;

Abstract

Let : [0, 1] [0, ) [0, ) be continuous and a C([0, 1], [0, )),and let (0, 1) with 0 < {\xi} < < … < < 1, , [0, ) with 0 < / < 1 and < l. This paper is concerned with the following m-point boundary value problem: ″(t)＋a(t) (t.(t))＝0,t (0,1), '(0)＝ /'(),(1)＝(). The existence, multiplicity and uniqueness of positive solutions of this problem are discussed with the help of two fixed point theorems in cones, respectively.

Keywords

m-point boundary value problem;existence of positive solutions;multiplicity, uniqueness;

Language

English

Cited by

1.

References

1.

C. P. Gupta, A generalized multi-point boundary value problem for second order ordinary differential equations, Appl. Math. Comput. 89 (1998), 133–46

2.

Ruyun Ma, Existence theorems for a second order m-point boundary value problem, J. Math. Anal. Appl. 211 (1997), 545–55

3.

W. Feng and J. R. L. Webb, Solvability of a m-point boundary value problems with nonlinear growth, J. Math. Anal. Appl. 212 (1997), 467–80

4.

Ruyun Ma and Nelson Castaneda, Existence of solutions of nonlinear m-point boundary-value problems, J. Math. Anal. Appl. 256 (2001), 556–67

5.

Qingliu Yao, Existence and multiplicity of positive radial solutions for a class of nonlinear elliptic equations in annular domains, Chinese Ann. Math. 22 (2001), 633–38

6.

Fuyi Li, Jinfeng Feng and Peilong Shen, The fixed point theorem and application for some decreasing operator, Acta. Math. Sinica. 42 (1999), 193–96

7.

L. H. Erbe, S. Hu and H. Wang, Multiplicity positive solutions of some boundary value problems, J. Math. Anal. Appl 184 (1994), 640–48

8.

D. J. Guo and V. Lakshmikantham, Nonlinear Problems in Abstract Cones, Aca-demic Press, San Diego, 1998.

9.

H. Amman, Fixed point equations and nonlinear eigenvalue problems in ordered Banach spaces, SIAM. Rev. 18 (1976), 620–09

10.

Zhang Zhitao, New fixed point theorems of mixed monotone operators and appli-cations, J. Math. Anal. Appl. 204 (1996), 307–19