Uniqueness implies existence and uniqueness conditions for nonlocal boundary value problems for nth order differential equations

Journal of Mathematical Analysis and Applications

Volumn 331, Issue 1, 2007, Pages 240-247

  Eloe, Paul W ^a   Henderson, Johnny ^b  

^a University of Dayton   (United States)

^b BAYLOR UNIVERSITY   (United States)

Author keywords

Boundary value problem; Existence; Nonlocal; Uniqueness

Indexed keywords

EID: 33947119143     PISSN: 0022247X     EISSN: 10960813     Source Type: Journal    
DOI: 10.1016/j.jmaa.2006.08.087     Document Type: Article

References (20)

1. S. Clark, J. Henderson, Uniqueness implies existence and uniqueness criterion for nonlocal boundary value problems for third order differential equations, Proc. Amer. Math. Soc., in press
2. Harris G.A., Henderson J., Lanz A., and Yin W.K.C. Third order right focal boundary value problems on a time scale. J. Difference Equ. Appl. 12 (2006) 525-533
3. Hartman P. Unrestricted n-parameter families. Rend. Circ. Mat. Palermo (2) 7 (1958) 123-142
4. Hartman P. On n-parameter families and interpolation problems for nonlinear differential equations. Trans. Amer. Math. Soc. 154 (1971) 201-226
5. Henderson J. Uniqueness of solutions of right focal point boundary value problems. J. Differential Equations 41 (1981) 218-227
6. Henderson J. Existence of solutions of right focal point boundary value problems. Nonlinear Anal. 5 (1981) 989-1002
7. Henderson J. Existence theorems for boundary value problems for nth order nonlinear difference equations. SIAM J. Math. Anal. 20 (1989) 468-478
8. Henderson J. Focal boundary value problems for nonlinear difference equations, I. J. Math. Anal. Appl. 141 (1989) 559-567
9. Henderson J. Focal boundary value problems for nonlinear difference equations, II. J. Math. Anal. Appl. 141 (1989) 568-579
10. Henderson J. Uniqueness implies existence for three-point boundary value problems for second order differential equations. Appl. Math. Lett. 18 (2005) 905-909
11. Henderson J., Karna B., and Tisdell C.C. Existence of solutions for three-point boundary value problems for second order equations. Proc. Amer. Math. Soc. 133 (2005) 1365-1369
12. J. Henderson, D. Ma, Uniqueness of solutions for fourth order nonlocal boundary value problems, Bound. Value Probl., in press
13. Henderson J., and Yin W.K.C. Existence of solutions for fourth order boundary value problems on a time scale. J. Difference Equ. Appl. 9 (2003) 15-28
14. Jackson L.K. Uniqueness of solutions of boundary value problems for ordinary differential equations. SIAM J. Appl. Math. 24 (1973) 525-538
15. Jackson L.K. Existence and uniqueness of solutions for third order differential equations. J. Differential Equations 13 (1973) 432-437
16. Klaasen G. Existence theorems for boundary value problems for nth order ordinary differential equations. Rocky Mountain J. Math. 3 (1973) 457-472
17. Lasota A., and Opial Z. On the existence and uniqueness of solutions of a boundary value problem for an ordinary second order differential equation. Colloq. Math. 18 (1967) 1-5
18. Peterson A.C. Existence-uniqueness for focal-point boundary value problems. SIAM J. Math. Anal. 12 (1982) 173-185
19. Schrader K. Uniqueness implies existence for solutions of nonlinear boundary value problems. Abstracts Amer. Math. Soc. 6 (1985) 235
20. Spanier E.H. Algebraic Topology (1966), McGraw-Hill, New York