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POSITIVE SOLUTIONS FOR A SYSTEM OF SINGULAR SECOND ORDER NONLOCAL BOUNDARY VALUE PROBLEMS
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 Title & Authors
POSITIVE SOLUTIONS FOR A SYSTEM OF SINGULAR SECOND ORDER NONLOCAL BOUNDARY VALUE PROBLEMS
Asif, Naseer Ahmad; Eloe, Paul W.; Khan, Rahmat Ali;
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 Abstract
Sufficient conditions for the existence of positive solutions for a coupled system of nonlinear nonlocal boundary value problems of the type -x"(t) = f(t, y(t)), t (0, 1), -y"(t) = g(t, x(t)), t (0, 1), x(0) = y(0) = 0, x(1) = , y(1) = , are obtained. The nonlinearities f, g : (0,1) (0, ) (0, ) are continuous and may be singular at t = 0, t = 1, x = 0, or y = 0. The parameters , , satisfy (0,1), 0 < < . An example is provided to illustrate the results.
 Keywords
positive solutions;singular system of ordinary differential equations;three-point nonlocal boundary value problem;
 Language
English
 Cited by
1.
Positive solutions to singular system with four-point coupled boundary conditions, Journal of Mathematical Analysis and Applications, 2012, 386, 2, 848  crossref(new windwow)
2.
On two systems of non-resonant nonlocal boundary value problems, Analele Universitatii "Ovidius" Constanta - Seria Matematica, 2013, 21, 3  crossref(new windwow)
 References
1.
R. P. Agarwal and D. O’Regan, Singular Differential and Integral Equations with Applications, Kluwer Academic Publishers, Dordrecht, 2003.

2.
A. V. Bicadze and A. A. Samarskii, Some elementary generalizations of linear elliptic boundary value problems, Dokl. Akad. Nauk SSSR 185 (1969), 739-740.

3.
A. V. Bitsadze, On the theory of nonlocal boundary value problems, Dokl. Akad. Nauk SSSR 277 (1984), no. 1, 17-19.

4.
A. V. Bitsadze, A class of conditionally solvable nonlocal boundary value problems for harmonic functions, Dokl. Akad. Nauk SSSR 280 (1985), no. 3, 521-524.

5.
L. E. Bobisud, Existence of solutions for nonlinear singular boundary value problems, Appl. Anal. 35 (1990), no. 1-4, 43-57. crossref(new window)

6.
W. Cheung and P. Wong, Fixed-sign solutions for a system of singular focal boundary value problems, J. Math. Anal. Appl. 329 (2007), no. 2, 851-869. crossref(new window)

7.
R. Dalmasso, Existence and uniqueness of positive radial solutions for the Lane-Emden system, Nonlinear Anal. 57 (2004), no. 3, 341-348. crossref(new window)

8.
D. Guo and V. Lakshmikantham, Nonlinear Problems in Abstract Cones, Academic Press, Inc., Boston, MA, 1988.

9.
C. P. Gupta, Solvability of a three-point nonlinear boundary value problem for a second order ordinary differential equation, J. Math. Anal. Appl. 168 (1992), no. 2, 540-551. crossref(new window)

10.
V. A. Il’in and E. I. Moiseev, A nonlocal boundary value problem of the first kind for the Sturm-Liouville operator in differential and difference interpretations, Differentsial’nye Uravneniya 23 (1987), no. 7, 1198-1207.

11.
V. A. Il’in and E. I. Moiseev, A nonlocal boundary value problem of the second kind for the Sturm-Liouville operator, Differentsial’nye Uravneniya 23 (1987), no. 8, 1422-1431, 1471.

12.
P. Kang and Z. Wei, Three positive solutions of singular nonlocal boundary value problems for systems of nonlinear second-order ordinary differential equations, Nonlinear Anal. 70 (2009), no. 1, 444-451. crossref(new window)

13.
P. Kelevedjiev, Nonnegative solutions to some singular second-order boundary value problems, Nonlinear Anal. 36 (1999), no. 4, Ser. A: Theory Methods, 481-494. crossref(new window)

14.
B. Liu, Positive solutions of a nonlinear three-point boundary value problem, Comput. Math. Appl. 44 (2002), no. 1-2, 201-211. crossref(new window)

15.
B. Liu, L. Liu, and Y. Wu, Positive solutions for singular second order three-point boundary value problems, Nonlinear Anal. 66 (2007), no. 12, 2756-2766. crossref(new window)

16.
B. Liu, L. Liu, and Y. Wu, Positive solutions for singular systems of three-point boundary value problems, Comput. Math. Appl. 53 (2007), no. 9, 1429-1438. crossref(new window)

17.
R. Ma, Positive solutions of a nonlinear three-point boundary-value problem, Electron. J. Differential Equations 1999 (1999), no. 34, 8 pp.

18.
M. Moshinsky, Sobre los problems de conditions a la frontiera en una dimension de caracteristicas discontinuas, Bol. Soc. Mat. Mexicana 7 (1950), 1-25.

19.
T. Timoshenko, Theory of Elastic Theory, McGraw-Hill, New York, 1971.

20.
J. R. L. Webb, Positive solutions of some three point boundary value problems via fixed point index theory, Nonlinear Anal. 47 (2001), no. 7, 4319-4332. crossref(new window)

21.
S. Xie and J. Zhu, Positive solutions of boundary value problems for system of nonlinear fourth-order differential equations, Bound. Value Probl. 2007 (2007), Art. ID 76493, 12 pp.

22.
Z. Zhao, Solutions and Green’s functions for some linear second-order three-point boundary value problems, Comput. Math. Appl. 56 (2008), no. 1, 104-113. crossref(new window)

23.
Y. Zhou and Y. Xu, Positive solutions of three-point boundary value problems for systems of nonlinear second order ordinary differential equations, J. Math. Anal. Appl. 320 (2006), no. 2, 578-590. crossref(new window)