Constructive proof for existence of nonlinear two-point boundary value problems

Applied Mathematics and Computation

Volumn 215, Issue 5, 2009, Pages 1937-1948

  Jiang, Wei ^a   Cui, Minggen ^a  

^a HARBIN INSTITUTE OF TECHNOLOGY   (China)

Author keywords

Boundary value problems (BVPs); Existence; Reproducing kernel space

Indexed keywords

CONSTRUCTIVE PROOF; EXACT SOLUTION; EXISTENCE; EXISTENCE OF SOLUTIONS; EXISTENCE RESULTS; LINEAR PROBLEMS; NONLINEAR PROBLEMS; REPRODUCING KERNEL SPACE; RIGHT-HAND SIDES; SECOND ORDERS; SINGULAR KERNEL; STABILITY ANALYSIS; TWO-POINT BOUNDARY VALUE PROBLEM;

BOUNDARY VALUE PROBLEMS; LINEARIZATION; ORDINARY DIFFERENTIAL EQUATIONS;

PROBLEM SOLVING;

EID: 70349887748     PISSN: 00963003     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.amc.2009.07.044     Document Type: Article

References (29)

1. Henderson J., Peterson A., and Tisdell C.C. On the existence and uniqueness of solutions to boundary value problems on time scales. Adv. Differ. Equat. 2 (2004) 93-109
2. Amster P., Rogers C., and Tisdell C.C. Existence of solutions to boundary value problems for dynamic systems on time scales. J. Math. Anal. Appl. 308 (2005) 565-577
3. Tisdell C.C. Existence of solutions to first-order periodic boundary value problems. J. Math. Anal. Appl. 323 (2006) 1325-1332
4. Henderson J., and Tisdell C.C. Dynamic boundary value problems of the second-order: Bernstein-Nagumo conditions and solvability. Nonlinear Anal. 67 (2007) 1374-1386
5. Henderson J., and Thompson H.B. Existence of multiple solutions for second order boundary value problems. J. Differ. Equat. 166 (2000) 443-454
6. Lian W.-C., Chou C.-C., Liu C.-T., and Wong F.-H. Existence of solutions for nonlinear BVPs of second-order differential equations on measure chains. Math. Comput. Model. 34 (2001) 821-837
7. Tao Y., and Gao G. Existence, uniqueness and approximation of classical solutions to nonlinear two-point boundary value problems. Nonlinear Anal. 50 (2002) 981-994
8. Liu Y., and Ge W. Twin positive solutions of boundary value problems for finite difference equations with p-Laplacian operator. J. Math. Anal. Appl. 278 (2003) 551-561
9. Aykut N. Existence of positive solutions for boundary value problems of second order functional difference equations. Comput. Math. Appl. 48 (2004) 517-527
10. Misir A., and Tiryaki A. More on the explicit solutions for a second order nonlinear boundary value problem. Appl. Math. Lett. 21 (2008) 1204-1208
11. Kong Q. Existence and nonexistence of solutions of second-order nonlinear boundary value problems. Nonlinear Anal. 66 (2007) 2635-2651
12. Liu Y. Studies on Neumann-type boundary value problems for second-order nonlinear p-Laplacian-like functional differential equations. Nonlinear Anal.: Real World Appl. 10 (2009) 333-344
13. Li F., Liang Z., and Zhang Q. Existence of solutions to a class of nonlinear second order two-point boundary value problems. J. Math. Anal. Appl. 312 (2005) 357-373
14. Jiang L., and Zhou Z. Existence of nontrivial solutions for discrete nonlinear two point boundary value problems. Appl. Math. Comput. 180 (2006) 318-329
15. Tirmizi I.A., and Twizell E.H. Higher-order finite difference methods for nonlinear second-order two-point boundary-value problems. Appl. Math. Lett. 15 (2002) 897-902
16. Elbarbary E.M.E., and El-Kady M. Chebyshev finite difference approximation for the boundary value problems. Appl. Math. Comput. 139 (2003) 513-523
17. Ha S.N. A nonlinear shooting method for two-point boundary value problems. Comput. Math. Appl. 42 (2001) 1411-1420
18. Liang H., and Weng P. Existence of positive solutions for boundary value problems of second order functional difference equations. Nonlinear Anal. 326 (2007) 520-551
19. Cherpion M., De Coster C., and Habets P. A constructive monotone iterative method for second-order BVP in the presence of lower and upper solutions. Appl. Math. Comput. 123 (2001) 75-91
20. Dang Quang A. Iterative method for solving a nonlinear boundary value problem. Appl. Math. Comput. 190 (2007) 1675-1682
21. Ahmad B., Nieto J., and Shahzad N. The Bellman-Kalaba-Lakshmikantham quasilinearization method for Neumann problems. J. Math. Anal. Appl. 257 (2001) 356-363
22. Ahmad B., Ali Khan R., and Eloe P.W. Generalized quasilinearization method for a second order three point boundary-value problem with nonlinear boundary conditions. Electron. J. Differ. Equat. 2002 (2002) 1-12
23. Ahmad B., Nieto J.J., and Shahzad N. Generalized quasilinearization method for mixed boundary value problems. Appl. Math. Comput. 133 (2002) 423-429
24. Vatsala A.S., and Melton T.G. Generalized quasilinearization method and higher order of convergence for second-order boundary value problems. Bound. Value Prob. 2006 (2006) 1-15
25. Khan R.A. The generalized quasilinearization technique for a second order differential equation with separated boundary conditions. Math. Comput. Model. 43 (2006) 727-742
26. Jiang W., and Cui M. The exact solution and stability analysis for integral equation of third or first kind with singular kernel. Appl. Math. Comput. 202 2 (2008) 666-674
27. Chen Z., and Lin Y. The exact solution of a linear integral equation with weakly singular kernel. J. Math. Anal. Appl. 344 (2008) 726-734
28. Cui M., and Lin Y. Nonlinear Numerical Analysis in the Reproducing Kernel Space (2009), Nova Science Publisher, New York
29. Lu-Feng Mo, Shu-Qiang Wang, A variational approach to nonlinear two-point boundary value problems, Nonlinear Anal.: Theory Methods Appl. (2008), doi: 10.1016/j.na.2008.12.006.